Master File
Joanna Duran, Nikhil Gupta, Max Moro
2019-03-28 22:08:34
User Inputs
output.var = params$output.var
transform.abs = FALSE
log.pred = params$log.pred
norm.pred = params$norm.pred
eda = params$eda
algo.forward.caret = params$algo.forward.caret
algo.backward.caret = params$algo.backward.caret
algo.stepwise.caret = params$algo.stepwise.caret
algo.LASSO.caret = params$algo.LASSO.caret
algo.LARS.caret = params$algo.LARS.caret
message("Parameters used for training/prediction: ")## Parameters used for training/prediction:str(params)## List of 9
## $ output.var : chr "y3"
## $ log.pred : logi TRUE
## $ norm.pred : logi FALSE
## $ eda : logi FALSE
## $ algo.forward.caret : logi TRUE
## $ algo.backward.caret: logi TRUE
## $ algo.stepwise.caret: logi TRUE
## $ algo.LASSO.caret : logi TRUE
## $ algo.LARS.caret : logi TRUE# Setup Labels
#output.var.tr = if (log.pred == TRUE) paste0(output.var,'.log') else output.var.tr = output.var
output.var.tr = if (log.pred == TRUE) paste0(output.var,'.cuberoot') else output.var.tr = output.var
# output.var.tr = if (norm.pred == TRUE) paste0(output.var,'.bestnorm') else output.var.tr = output.varLoading Data
feat = read.csv('../../Data/features_highprec.csv')
labels = read.csv('../../Data/labels.csv')
predictors = names(dplyr::select(feat,-JobName))
data.ori = inner_join(feat,labels,by='JobName')
#data.ori = inner_join(feat,select_at(labels,c('JobName',output.var)),by='JobName')Data validation
cc = complete.cases(data.ori)
data.notComplete = data.ori[! cc,]
data = data.ori[cc,] %>% select_at(c(predictors,output.var,'JobName'))
message('Original cases: ',nrow(data.ori))## Original cases: 10000message('Non-Complete cases: ',nrow(data.notComplete))## Non-Complete cases: 3020message('Complete cases: ',nrow(data))## Complete cases: 6980summary(dplyr::select_at(data,c('JobName',output.var)))## JobName y3
## Job_00001: 1 Min. : 95.91
## Job_00002: 1 1st Qu.:118.29
## Job_00003: 1 Median :124.03
## Job_00004: 1 Mean :125.40
## Job_00007: 1 3rd Qu.:131.06
## Job_00008: 1 Max. :193.73
## (Other) :6974Output Variable
The Output Variable y3 shows right skewness, so will proceed with a log transformation
Histogram
df=gather(select_at(data,output.var))
ggplot(df, aes(x=value)) +
geom_histogram(aes(y=..density..),bins = 50,fill='light blue') +
geom_density() 
#stat_function(fun = dnorm, n = 100, args = list(mean = mean(df$value), sd = sd(df$value))) QQPlot
ggplot(gather(select_at(data,output.var)), aes(sample=value)) +
stat_qq() +
facet_wrap(~key, scales = 'free',ncol=4)
Trasformation of Output Variable from y3 to y3.cuberoot
#if(log.pred==TRUE) data[[output.var.tr]] = log(data[[output.var]],10) else
if(log.pred==TRUE) data[[output.var.tr]] = (data[[output.var]])^(1/3) else
data[[output.var.tr]] = data[[output.var]]
df=gather(select_at(data,c(output.var,output.var.tr)))
ggplot(df, aes(value)) +
geom_histogram(aes(y=..density..),bins = 50,fill='light blue') +
geom_density() +
# stat_function(fun = dnorm, n = 100, args = list(mean = mean(df$value), sd = sd(df$value)))
facet_wrap(~key, scales = 'free',ncol=2)
ggplot(gather(select_at(data,c(output.var,output.var.tr))), aes(sample=value)) +
stat_qq() +
facet_wrap(~key, scales = 'free',ncol=4)
Best Normalizator y3
Normalization of y3 using bestNormalize package. (suggested orderNorm) This is cool, but I think is too far for the objective of the project
if (norm.pred == TRUE){
t=bestNormalize::bestNormalize(data[[output.var]])
t
qqnorm(data[[output.var]])
qqnorm(predict(t))
data[[output.var.tr]] = predict(t)
}orderNorm() is a rank-based procedure by which the values of a vector are mapped to their percentile, which is then mapped to the same percentile of the normal distribution. Without the presence of ties, this essentially guarantees that the transformation leads to a uniform distribution
Predictors
Feature Engineering
data$x2byx1 = data$x2/data$x1
data$x6byx5 = data$x6/data$x5
data$x9byx7 = data$x9/data$x7
data$x10byx8 = data$x10/data$x8
data$x14byx12 = data$x14/data$x12
data$x15byx13 = data$x15/data$x13
data$x17byx16 = data$x17/data$x16
data$x19byx18 = data$x19/data$x18
data$x21byx20 = data$x21/data$x20
data$x23byx22 = data$x23/data$x22
data$x1log = log(data$x1)
data$x2log = log(data$x2)
data$x5log = log(data$x5)
data$x6log = log(data$x6)
data$x7log = log(data$x7)
data$x9log = log(data$x9)
data$x8log = log(data$x8)
data$x10log = log(data$x10)
data$x12log = log(data$x12)
data$x14log = log(data$x14)
data$x13log = log(data$x13)
data$x15log = log(data$x15)
data$x16log = log(data$x16)
data$x17log = log(data$x17)
data$x18log = log(data$x18)
data$x19log = log(data$x19)
data$x20log = log(data$x20)
data$x21log = log(data$x21)
data$x22log = log(data$x22)
data$x23log = log(data$x23)data$x11log = log(data$x11)data$x1sqinv = 1/(data$x1)^2
data$x5sqinv = 1/(data$x5)^2
data$x7sqinv = 1/(data$x7)^2
data$x8sqinv = 1/(data$x8)^2
data$x12sqinv = 1/(data$x12)^2
data$x13sqinv = 1/(data$x13)^2
data$x16sqinv = 1/(data$x16)^2
data$x18sqinv = 1/(data$x18)^2
data$x20sqinv = 1/(data$x20)^2
data$x22sqinv = 1/(data$x22)^2 predictors## [1] "x1" "x2" "x3" "x4" "x5" "x6" "x7" "x8" "x9" "x10" "x11"
## [12] "x12" "x13" "x14" "x15" "x16" "x17" "x18" "x19" "x20" "x21" "x22"
## [23] "x23" "stat1" "stat2" "stat3" "stat4" "stat5" "stat6" "stat7" "stat8" "stat9" "stat10"
## [34] "stat11" "stat12" "stat13" "stat14" "stat15" "stat16" "stat17" "stat18" "stat19" "stat20" "stat21"
## [45] "stat22" "stat23" "stat24" "stat25" "stat26" "stat27" "stat28" "stat29" "stat30" "stat31" "stat32"
## [56] "stat33" "stat34" "stat35" "stat36" "stat37" "stat38" "stat39" "stat40" "stat41" "stat42" "stat43"
## [67] "stat44" "stat45" "stat46" "stat47" "stat48" "stat49" "stat50" "stat51" "stat52" "stat53" "stat54"
## [78] "stat55" "stat56" "stat57" "stat58" "stat59" "stat60" "stat61" "stat62" "stat63" "stat64" "stat65"
## [89] "stat66" "stat67" "stat68" "stat69" "stat70" "stat71" "stat72" "stat73" "stat74" "stat75" "stat76"
## [100] "stat77" "stat78" "stat79" "stat80" "stat81" "stat82" "stat83" "stat84" "stat85" "stat86" "stat87"
## [111] "stat88" "stat89" "stat90" "stat91" "stat92" "stat93" "stat94" "stat95" "stat96" "stat97" "stat98"
## [122] "stat99" "stat100" "stat101" "stat102" "stat103" "stat104" "stat105" "stat106" "stat107" "stat108" "stat109"
## [133] "stat110" "stat111" "stat112" "stat113" "stat114" "stat115" "stat116" "stat117" "stat118" "stat119" "stat120"
## [144] "stat121" "stat122" "stat123" "stat124" "stat125" "stat126" "stat127" "stat128" "stat129" "stat130" "stat131"
## [155] "stat132" "stat133" "stat134" "stat135" "stat136" "stat137" "stat138" "stat139" "stat140" "stat141" "stat142"
## [166] "stat143" "stat144" "stat145" "stat146" "stat147" "stat148" "stat149" "stat150" "stat151" "stat152" "stat153"
## [177] "stat154" "stat155" "stat156" "stat157" "stat158" "stat159" "stat160" "stat161" "stat162" "stat163" "stat164"
## [188] "stat165" "stat166" "stat167" "stat168" "stat169" "stat170" "stat171" "stat172" "stat173" "stat174" "stat175"
## [199] "stat176" "stat177" "stat178" "stat179" "stat180" "stat181" "stat182" "stat183" "stat184" "stat185" "stat186"
## [210] "stat187" "stat188" "stat189" "stat190" "stat191" "stat192" "stat193" "stat194" "stat195" "stat196" "stat197"
## [221] "stat198" "stat199" "stat200" "stat201" "stat202" "stat203" "stat204" "stat205" "stat206" "stat207" "stat208"
## [232] "stat209" "stat210" "stat211" "stat212" "stat213" "stat214" "stat215" "stat216" "stat217"controlled.vars = colnames(data)[grep("^x",colnames(data))]
stat.vars = colnames(data)[grep("^stat",colnames(data))]
predictors = c(controlled.vars,stat.vars)
predictors## [1] "x1" "x2" "x3" "x4" "x5" "x6" "x7" "x8" "x9" "x10"
## [11] "x11" "x12" "x13" "x14" "x15" "x16" "x17" "x18" "x19" "x20"
## [21] "x21" "x22" "x23" "x2byx1" "x6byx5" "x9byx7" "x10byx8" "x14byx12" "x15byx13" "x17byx16"
## [31] "x19byx18" "x21byx20" "x23byx22" "x1log" "x2log" "x5log" "x6log" "x7log" "x9log" "x8log"
## [41] "x10log" "x12log" "x14log" "x13log" "x15log" "x16log" "x17log" "x18log" "x19log" "x20log"
## [51] "x21log" "x22log" "x23log" "x11log" "x1sqinv" "x5sqinv" "x7sqinv" "x8sqinv" "x12sqinv" "x13sqinv"
## [61] "x16sqinv" "x18sqinv" "x20sqinv" "x22sqinv" "stat1" "stat2" "stat3" "stat4" "stat5" "stat6"
## [71] "stat7" "stat8" "stat9" "stat10" "stat11" "stat12" "stat13" "stat14" "stat15" "stat16"
## [81] "stat17" "stat18" "stat19" "stat20" "stat21" "stat22" "stat23" "stat24" "stat25" "stat26"
## [91] "stat27" "stat28" "stat29" "stat30" "stat31" "stat32" "stat33" "stat34" "stat35" "stat36"
## [101] "stat37" "stat38" "stat39" "stat40" "stat41" "stat42" "stat43" "stat44" "stat45" "stat46"
## [111] "stat47" "stat48" "stat49" "stat50" "stat51" "stat52" "stat53" "stat54" "stat55" "stat56"
## [121] "stat57" "stat58" "stat59" "stat60" "stat61" "stat62" "stat63" "stat64" "stat65" "stat66"
## [131] "stat67" "stat68" "stat69" "stat70" "stat71" "stat72" "stat73" "stat74" "stat75" "stat76"
## [141] "stat77" "stat78" "stat79" "stat80" "stat81" "stat82" "stat83" "stat84" "stat85" "stat86"
## [151] "stat87" "stat88" "stat89" "stat90" "stat91" "stat92" "stat93" "stat94" "stat95" "stat96"
## [161] "stat97" "stat98" "stat99" "stat100" "stat101" "stat102" "stat103" "stat104" "stat105" "stat106"
## [171] "stat107" "stat108" "stat109" "stat110" "stat111" "stat112" "stat113" "stat114" "stat115" "stat116"
## [181] "stat117" "stat118" "stat119" "stat120" "stat121" "stat122" "stat123" "stat124" "stat125" "stat126"
## [191] "stat127" "stat128" "stat129" "stat130" "stat131" "stat132" "stat133" "stat134" "stat135" "stat136"
## [201] "stat137" "stat138" "stat139" "stat140" "stat141" "stat142" "stat143" "stat144" "stat145" "stat146"
## [211] "stat147" "stat148" "stat149" "stat150" "stat151" "stat152" "stat153" "stat154" "stat155" "stat156"
## [221] "stat157" "stat158" "stat159" "stat160" "stat161" "stat162" "stat163" "stat164" "stat165" "stat166"
## [231] "stat167" "stat168" "stat169" "stat170" "stat171" "stat172" "stat173" "stat174" "stat175" "stat176"
## [241] "stat177" "stat178" "stat179" "stat180" "stat181" "stat182" "stat183" "stat184" "stat185" "stat186"
## [251] "stat187" "stat188" "stat189" "stat190" "stat191" "stat192" "stat193" "stat194" "stat195" "stat196"
## [261] "stat197" "stat198" "stat199" "stat200" "stat201" "stat202" "stat203" "stat204" "stat205" "stat206"
## [271] "stat207" "stat208" "stat209" "stat210" "stat211" "stat212" "stat213" "stat214" "stat215" "stat216"
## [281] "stat217"All predictors show a Fat-Tail situation, where the two tails are very tall, and a low distribution around the mean. The orderNorm transformation can help (see [Best Normalizator] section)
Interesting Predictors
Histograms
if (eda == TRUE){
cols = c('x11','x18','stat98','x7','stat110')
df=gather(select_at(data,cols))
ggplot(df, aes(value)) +
geom_histogram(aes(y=..density..),bins = 50,fill='light blue') +
geom_density() +
# stat_function(fun = dnorm, n = 100, args = list(mean = mean(df$value), sd = sd(df$value)))
facet_wrap(~key, scales = 'free',ncol=3)
# ggplot(gather(select_at(data,cols)), aes(sample=value)) +
# stat_qq()+
# facet_wrap(~key, scales = 'free',ncol=2)
lapply(select_at(data,cols),summary)
}Scatter plot vs. output variable **y3.cuberoot
if (eda == TRUE){
d = gather(dplyr::select_at(data,c(cols,output.var.tr)),key=target,value=value,-!!output.var.tr)
ggplot(data=d, aes_string(x='value',y=output.var.tr)) +
geom_point(color='light green',alpha=0.5) +
geom_smooth() +
facet_wrap(~target, scales = 'free',ncol=3)
}All Predictors
Histograms
All indicators have a strong indication of Fat-Tails
if (eda == TRUE){
df=gather(select_at(data,predictors))
ggplot(df, aes(value)) +
geom_histogram(aes(y=..density..),bins = 50,fill='light blue') +
geom_density() +
# stat_function(fun = dnorm, n = 100, args = list(mean = mean(df$value), sd = sd(df$value)))
facet_wrap(~key, scales = 'free',ncol=4)
}Correlations
With Output Variable
if (eda == TRUE){
#chart.Correlation(select(data,-JobName), pch=21)
# https://stackoverflow.com/questions/27034655/how-to-use-dplyrarrangedesc-when-using-a-string-as-column-name
t=as.data.frame(round(cor(dplyr::select(data,-one_of(output.var.tr,'JobName'))
,select_at(data,output.var.tr)),4)) %>%
#rownames_to_column(var='variable') %>% filter(variable != !!output.var) %>% arrange(-y3.log)
rownames_to_column(var='variable') %>% filter(variable != !!output.var) %>% arrange(-!!sym(output.var.tr))
#DT::datatable(t)
message("Top Positive")
#kable(head(arrange(t,desc(y3.log)),20))
kable(head(arrange(t,desc(!!sym(output.var.tr))),20))
message("Top Negative")
#kable(head(arrange(t,y3.log),20))
kable(head(arrange(t,!!sym(output.var.tr)),20))
}Between All Variables
if (eda == TRUE){
#chart.Correlation(select(data,-JobName), pch=21)
t=as.data.frame(round(cor(dplyr::select(data,-one_of('JobName'))),4))
#DT::datatable(t,options=list(scrollX=T))
message("Showing only 10 variables")
kable(t[1:10,1:10])
}Scatter Plots with Output Variable
Scatter plots with all predictors and the output variable (y3.cuberoot)
if (eda == TRUE){
d = gather(dplyr::select_at(data,c(predictors,output.var.tr)),key=target,value=value,-!!output.var.tr)
ggplot(data=d, aes_string(x='value',y=output.var.tr)) +
geom_point(color='light blue',alpha=0.5) +
geom_smooth() +
facet_wrap(~target, scales = 'free',ncol=4)
}Multicollinearity - VIF
No Multicollinearity among predictors
Showing Top predictor by VIF Value
if (eda == TRUE){
vifDF = usdm::vif(select_at(data,predictors)) %>% arrange(desc(VIF))
head(vifDF,75)
}Feature Eng
- Square Root transformation for x18
data.tr=data %>%
mutate(x18.sqrt = sqrt(x18))
cols=c('x18','x18.sqrt')Comparing Pre and Post Transformation Density Plots
# ggplot(gather(select_at(data.tr,cols)), aes(value)) +
# geom_histogram(aes(y=..density..),bins = 50,fill='light blue') +
# geom_density() +
# facet_wrap(~key, scales = 'free',ncol=4)
d = gather(dplyr::select_at(data.tr,c(cols,output.var.tr)),key=target,value=value,-!!output.var.tr)
ggplot(data=d, aes_string(x='value',y=output.var.tr)) +
geom_point(color='light blue',alpha=0.5) +
geom_smooth() +
facet_wrap(~target, scales = 'free',ncol=4)## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'
#removing unwanted variables
data.tr=data.tr %>%
#dplyr::select_at(names(data.tr)[! names(data.tr) %in% c('x18','y3','JobName')])
dplyr::select_at(names(data.tr)[! names(data.tr) %in% c('JobName')])
data=data.tr
label.names=output.var.trModeling
PCA
# 0 for no interaction,
# 1 for Full 2 way interaction and
# 2 for Selective 2 way interaction
# 3 for Selective 3 way interaction
InteractionMode = 2
pca.vars = names(data)
pca.vars = pca.vars[!pca.vars %in% label.names]
# http://sshaikh.org/2015/05/06/parallelize-machine-learning-in-r-with-multi-core-cpus/
# #cl <- makeCluster(ceiling(detectCores()*0.5)) # use 75% of cores only, leave rest for other tasks
cl <- makeCluster(detectCores()*0.75) # use 75% of cores only, leave rest for other tasks
registerDoParallel(cl)
if(InteractionMode == 1){
pca.formula =as.formula(paste0('~(',paste0(pca.vars, collapse ='+'),')^2'))
pca.model = prcomp(formula=pca.formula,data=data[,pca.vars],center=T,scale.=T,retx = T)
#saveRDS(pca.model,'pca.model.rds')
}
if (InteractionMode == 0){
pca.model = prcomp(x=data[,pca.vars],center=T,scale.=T,retx = T)
}
if (InteractionMode >= 2 & InteractionMode <= 3){
controlled.vars = pca.vars[grep("^x",pca.vars)]
stat.vars = pca.vars[grep("^stat",pca.vars)]
if (InteractionMode >= 2){
interaction.form = paste0('~(',paste0(controlled.vars, collapse ='+'),')^2')
}
if (InteractionMode >= 3){
interaction.form = paste0('~(',paste0(controlled.vars, collapse ='+'),')^3')
}
no.interact.form = paste0(stat.vars, collapse ='+')
pca.formula = as.formula(paste(interaction.form, no.interact.form, sep = "+"))
pca.model = prcomp(formula=pca.formula,data=data[,pca.vars],center=T,scale.=T,retx = T)
}
stopCluster(cl)
registerDoSEQ() # register sequential engine in case you are not using this function anymoretargetCumVar = .9
pca.model$var = pca.model$sdev ^ 2 #eigenvalues
pca.model$pvar = pca.model$var / sum(pca.model$var)
pca.model$cumpvar = cumsum(pca.model$pvar )
pca.model$pcaSel = pca.model$cumpvar<=targetCumVar
pca.model$pcaSelCount = sum(pca.model$pcaSel)
pca.model$pcaSelTotVar = sum(pca.model$pvar[pca.model$pcaSel])
message(pca.model$pcaSelCount, " PCAs justify ",percent(targetCumVar)," of the total Variance. (",percent(pca.model$pcaSelTotVar),")")## 164 PCAs justify 90.0% of the total Variance. (90.0%)plot(pca.model$var,xlab="Principal component", ylab="Proportion of variance explained", type='b')
plot(cumsum(pca.model$pvar ),xlab="Principal component", ylab="Cumulative Proportion of variance explained", ylim=c(0,1), type='b')
screeplot(pca.model,npcs = pca.model$pcaSelCount)
screeplot(pca.model,npcs = pca.model$pcaSelCount,type='lines')
#summary(pca.model)
#pca.model$rotation
#creating dataset
data.pca = dplyr::select(data,!!label.names) %>%
dplyr::bind_cols(dplyr::select(as.data.frame(pca.model$x)
,!!colnames(pca.model$rotation)[pca.model$pcaSel])
)Train Test Split
data.pca = data.pca[sample(nrow(data.pca)),] # randomly shuffle data
split = sample.split(data.pca[,label.names], SplitRatio = 0.8)
data.train = subset(data.pca, split == TRUE)
data.test = subset(data.pca, split == FALSE)Common Functions
plot.diagnostics <- function(model, train) {
plot(model)
residuals = resid(model) # Plotted above in plot(lm.out)
r.standard = rstandard(model)
r.student = rstudent(model)
df = data.frame(x=predict(model,train),y=r.student)
p=ggplot(data=df,aes(x=x,y=y)) +
geom_point(color='blue',alpha=0.5,shape=20,size=2) +
geom_hline(yintercept = 0,size=1)+
ylab("Student Residuals") +
xlab("Predicted Values")+
ggtitle("Student Residual Plot")
plot(p)
df = data.frame(x=predict(model,train),y=r.standard)
p=ggplot(data=df,aes(x=x,y=y)) +
geom_point(color='blue',alpha=0.5,shape=20,size=2) +
geom_hline(yintercept = c(-2,0,2),size=1)+
ylab("Student Residuals") +
xlab("Predicted Values")+
ggtitle("Student Residual Plot")
plot(p)
# Histogram
df=data.frame(r.student)
p=ggplot(data=df,aes(r.student)) +
geom_histogram(aes(y=..density..),bins = 50,fill='blue',alpha=0.6) +
stat_function(fun = dnorm, n = 100, args = list(mean = 0, sd = 1)) +
ylab("Density")+
xlab("Studentized Residuals")+
ggtitle("Distribution of Studentized Residuals")
plot(p)
# http://www.stat.columbia.edu/~martin/W2024/R7.pdf
# Influential plots
inf.meas = influence.measures(model)
# print (summary(inf.meas)) # too much data
# Leverage plot
lev = hat(model.matrix(model))
df=tibble::rownames_to_column(as.data.frame(lev),'id')
p=ggplot(data=df,aes(x=as.numeric(id),y=lev)) +
geom_point(color='blue',alpha=0.5,shape=20,size=2) +
ylab('Leverage - check') +
xlab('Index')
plot(p)
# Cook's Distance
cd = cooks.distance(model)
df=tibble::rownames_to_column(as.data.frame(cd),'id')
p=ggplot(data=df,aes(x=as.numeric(id),y=cd)) +
geom_point(color='blue',alpha=0.5,shape=20,size=2) +
geom_text(data=filter(df,cd>15/nrow(train)),aes(label=id),check_overlap=T,size=3,vjust=-.5)+
ylab('Cooks distances') +
geom_hline(yintercept = c(4/nrow(train),0),size=1)+
xlab('Index')
plot(p)
print (paste("Number of data points that have Cook's D > 4/n: ", length(cd[cd > 4/nrow(train)]), sep = ""))
print (paste("Number of data points that have Cook's D > 1: ", length(cd[cd > 1]), sep = ""))
return(cd)
}
# function to set up random seeds
# Based on http://jaehyeon-kim.github.io/2015/05/Setup-Random-Seeds-on-Caret-Package.html
setCaretSeeds <- function(method = "cv", numbers = 1, repeats = 1, tunes = NULL, seed = 1701) {
#B is the number of resamples and integer vector of M (numbers + tune length if any)
B <- if (method == "cv") numbers
else if(method == "repeatedcv") numbers * repeats
else NULL
if(is.null(length)) {
seeds <- NULL
} else {
set.seed(seed = seed)
seeds <- vector(mode = "list", length = B)
seeds <- lapply(seeds, function(x) sample.int(n = 1000000
, size = numbers + ifelse(is.null(tunes), 0, tunes)))
seeds[[length(seeds) + 1]] <- sample.int(n = 1000000, size = 1)
}
# return seeds
seeds
}
train.caret.glmselect = function(formula, data, method
,subopt = NULL, feature.names
, train.control = NULL, tune.grid = NULL, pre.proc = NULL){
if(is.null(train.control)){
train.control <- trainControl(method = "cv"
,number = 10
,seeds = setCaretSeeds(method = "cv"
, numbers = 10
, seed = 1701)
,search = "grid"
,verboseIter = TRUE
,allowParallel = TRUE
)
}
if(is.null(tune.grid)){
if (method == 'leapForward' | method == 'leapBackward' | method == 'leapSeq'){
tune.grid = data.frame(nvmax = 1:length(feature.names))
}
if (method == 'glmnet' && subopt == 'LASSO'){
# Will only show 1 Lambda value during training, but that is OK
# https://stackoverflow.com/questions/47526544/why-need-to-tune-lambda-with-carettrain-method-glmnet-and-cv-glmnet
# Another option for LASSO is this: https://github.com/topepo/caret/blob/master/RegressionTests/Code/lasso.R
lambda = 10^seq(-2,0, length =100)
alpha = c(1)
tune.grid = expand.grid(alpha = alpha,lambda = lambda)
}
if (method == 'lars'){
# https://github.com/topepo/caret/blob/master/RegressionTests/Code/lars.R
fraction = seq(0, 1, length = 100)
tune.grid = expand.grid(fraction = fraction)
pre.proc = c("center", "scale")
}
}
# http://sshaikh.org/2015/05/06/parallelize-machine-learning-in-r-with-multi-core-cpus/
# #cl <- makeCluster(ceiling(detectCores()*0.5)) # use 75% of cores only, leave rest for other tasks
cl <- makeCluster(detectCores()*0.75) # use 75% of cores only, leave rest for other tasks
registerDoParallel(cl)
set.seed(1)
# note that the seed has to actually be set just before this function is called
# settign is above just not ensure reproducibility for some reason
model.caret <- caret::train(formula
, data = data
, method = method
, tuneGrid = tune.grid
, trControl = train.control
, preProc = pre.proc
)
stopCluster(cl)
registerDoSEQ() # register sequential engine in case you are not using this function anymore
if (method == 'leapForward' | method == 'leapBackward' | method == 'leapSeq'){
print("All models results")
print(model.caret$results) # all model results
print("Best Model")
print(model.caret$bestTune) # best model
model = model.caret$finalModel
# Metrics Plot
dataPlot = model.caret$results %>%
gather(key='metric',value='value',-nvmax) %>%
dplyr::filter(metric %in% c('MAE','RMSE','Rsquared'))
metricsPlot = ggplot(data=dataPlot,aes(x=nvmax,y=value) ) +
geom_line(color='lightblue4') +
geom_point(color='blue',alpha=0.7,size=.9) +
facet_wrap(~metric,ncol=2,scales='free_y')+
theme_light()
plot(metricsPlot)
# Residuals Plot
# leap function does not support studentized residuals
dataPlot=data.frame(pred=predict(model.caret,data),res=resid(model.caret))
residPlot = ggplot(dataPlot,aes(x=pred,y=res)) +
geom_point(color='light blue',alpha=0.7) +
geom_smooth(method="lm")+
theme_light()
plot(residPlot)
residHistogram = ggplot(dataPlot,aes(x=res)) +
geom_histogram(aes(y=..density..),fill='light blue',alpha=1) +
#geom_density(color='lightblue4') +
stat_function(fun = dnorm, n = 100, args = list(mean = mean(dataPlot$res)
, sd = sd(dataPlot$res)),color='lightblue4')
theme_light()
plot(residHistogram)
id = rownames(model.caret$bestTune)
# Provides the coefficients of the best model
# regsubsets doens return a full model (see documentation of regsubset), so we need to recalcualte themodel
# https://stackoverflow.com/questions/13063762/how-to-obtain-a-lm-object-from-regsubsets
print("Coefficients of final model:")
coefs <- coef(model, id=id)
#calculate the model to the the coef intervals
nams <- names(coefs)
nams <- nams[!nams %in% "(Intercept)"]
response <- as.character(formula[[2]])
form <- as.formula(paste(response, paste(nams, collapse = " + "), sep = " ~ "))
mod <- lm(form, data = data)
#coefs
#coef(mod)
print(car::Confint(mod))
return(list(model = model,id = id, residPlot = residPlot, residHistogram=residHistogram
,modelLM=mod))
}
if (method == 'glmnet' && subopt == 'LASSO'){
print(model.caret)
print(plot(model.caret))
print(model.caret$bestTune)
print(model.caret$results)
model=model.caret$finalModel
# Metrics Plot
dataPlot = model.caret$results %>%
gather(key='metric',value='value',-lambda) %>%
dplyr::filter(metric %in% c('MAE','RMSE','Rsquared'))
metricsPlot = ggplot(data=dataPlot,aes(x=lambda,y=value) ) +
geom_line(color='lightblue4') +
geom_point(color='blue',alpha=0.7,size=.9) +
facet_wrap(~metric,ncol=2,scales='free_y')+
theme_light()
plot(metricsPlot)
# Residuals Plot
dataPlot=data.frame(pred=predict(model.caret,data),res=resid(model.caret))
residPlot = ggplot(dataPlot,aes(x=pred,y=res)) +
geom_point(color='light blue',alpha=0.7) +
geom_smooth(method="lm")+
theme_light()
plot(residPlot)
residHistogram = ggplot(dataPlot,aes(x=res)) +
geom_histogram(aes(y=..density..),fill='light blue',alpha=1) +
#geom_density(color='lightblue4') +
stat_function(fun = dnorm, n = 100, args = list(mean = mean(dataPlot$res)
, sd = sd(dataPlot$res)),color='lightblue4')
theme_light()
plot(residHistogram)
print("Coefficients")
#no interval for glmnet: https://stackoverflow.com/questions/39750965/confidence-intervals-for-ridge-regression
t=coef(model,s=model.caret$bestTune$lambda)
model.coef = t[which(t[,1]!=0),]
print(as.data.frame(model.coef))
id = NULL # not really needed but added for consistency
return(list(model = model.caret,id = id, residPlot = residPlot, metricsPlot=metricsPlot ))
}
if (method == 'lars'){
print(model.caret)
print(plot(model.caret))
print(model.caret$bestTune)
# Metrics Plot
dataPlot = model.caret$results %>%
gather(key='metric',value='value',-fraction) %>%
dplyr::filter(metric %in% c('MAE','RMSE','Rsquared'))
metricsPlot = ggplot(data=dataPlot,aes(x=fraction,y=value) ) +
geom_line(color='lightblue4') +
geom_point(color='blue',alpha=0.7,size=.9) +
facet_wrap(~metric,ncol=2,scales='free_y')+
theme_light()
plot(metricsPlot)
# Residuals Plot
dataPlot=data.frame(pred=predict(model.caret,data),res=resid(model.caret))
residPlot = ggplot(dataPlot,aes(x=pred,y=res)) +
geom_point(color='light blue',alpha=0.7) +
geom_smooth(method="lm")+
theme_light()
plot(residPlot)
residHistogram = ggplot(dataPlot,aes(x=res)) +
geom_histogram(aes(y=..density..),fill='light blue',alpha=1) +
#geom_density(color='lightblue4') +
stat_function(fun = dnorm, n = 100, args = list(mean = mean(dataPlot$res)
, sd = sd(dataPlot$res)),color='lightblue4')
theme_light()
plot(residHistogram)
print("Coefficients")
t=coef(model.caret$finalModel,s=model.caret$bestTune$fraction,mode='fraction')
model.coef = t[which(t!=0)]
print(model.coef)
id = NULL # not really needed but added for consistency
return(list(model = model.caret,id = id, residPlot = residPlot, residHistogram=residHistogram))
}
}
# https://stackoverflow.com/questions/48265743/linear-model-subset-selection-goodness-of-fit-with-k-fold-cross-validation
# changed slightly since call[[2]] was just returning "formula" without actually returnign the value in formula
predict.regsubsets <- function(object, newdata, id, formula, ...) {
#form <- as.formula(object$call[[2]])
mat <- model.matrix(formula, newdata) # adds intercept and expands any interaction terms
coefi <- coef(object, id = id)
xvars <- names(coefi)
return(mat[,xvars]%*%coefi)
}
test.model = function(model, test, level=0.95
,draw.limits = FALSE, good = 0.1, ok = 0.15
,method = NULL, subopt = NULL
,id = NULL, formula, feature.names, label.names
,transformation = NULL){
## if using caret for glm select equivalent functionality,
## need to pass formula (full is ok as it will select subset of variables from there)
if (is.null(method)){
pred = predict(model, newdata=test, interval="confidence", level = level)
}
if (method == 'leapForward' | method == 'leapBackward' | method == 'leapSeq'){
pred = predict.regsubsets(model, newdata = test, id = id, formula = formula)
}
if (method == 'glmnet' && subopt == 'LASSO'){
xtest = as.matrix(test[,feature.names])
pred=as.data.frame(predict(model, xtest))
}
if (method == 'lars'){
pred=as.data.frame(predict(model, newdata = test))
}
# Summary of predicted values
print ("Summary of predicted values: ")
print(summary(pred[,1]))
test.mse = mean((test[,label.names]-pred[,1])^2)
print (paste(method, subopt, "Test MSE:", test.mse, sep=" "))
test.rmse = sqrt(test.mse)
print (paste(method, subopt, "Test RMSE:", test.rmse, sep=" "))
if(log.pred == TRUE || norm.pred == TRUE){
# plot transformewd comparison first
df=data.frame(x=test[,label.names],y=pred[,1])
ggplot(df,aes(x=x,y=y)) +
geom_point(color='blue',alpha=0.5,shape=20,size=2) +
geom_abline(slope=1,intercept=0,color='black',size=1) +
#scale_y_continuous(limits=c(min(df),max(df)))+
xlab("Actual (Transformed)")+
ylab("Predicted (Transformed)")
}
if (log.pred == FALSE && norm.pred == FALSE){
x = test[,label.names]
y = pred[,1]
}
if (log.pred == TRUE){
# x = 10^test[,label.names]
# y = 10^pred[,1]
x = (test[,label.names])^3
y = (pred[,1])^3
}
if (norm.pred == TRUE){
x = predict(transformation, test[,label.names], inverse = TRUE)
y = predict(transformation, pred[,1], inverse = TRUE)
}
test.mse = mean((x-y)^2)
print (paste(method, subopt, "Test MSE (Org Scale):", test.mse, sep=" "))
test.rmse = sqrt(test.mse)
print (paste(method, subopt, "Test RMSE (Org Scale):", test.rmse, sep=" "))
df=data.frame(x,y)
ggplot(df,aes(x,y)) +
geom_point(color='blue',alpha=0.5,shape=20,size=2) +
geom_abline(slope=c(1+good,1-good,1+ok,1-ok)
,intercept=rep(0,4),color=c('dark green','dark green','dark red','dark red'),size=1,alpha=0.8) +
#scale_y_continuous(limits=c(min(df),max(df)))+
xlab("Actual")+
ylab("Predicted")
}Setup Formulae
n <- names(data.train)
formula <- as.formula(paste(paste(n[n %in% label.names], collapse = " + ")
," ~", paste(n[!n %in% label.names], collapse = " + ")))
grand.mean.formula = as.formula(paste(paste(n[n %in% label.names], collapse = " + ")," ~ 1"))
print(formula)## y3.cuberoot ~ PC1 + PC2 + PC3 + PC4 + PC5 + PC6 + PC7 + PC8 +
## PC9 + PC10 + PC11 + PC12 + PC13 + PC14 + PC15 + PC16 + PC17 +
## PC18 + PC19 + PC20 + PC21 + PC22 + PC23 + PC24 + PC25 + PC26 +
## PC27 + PC28 + PC29 + PC30 + PC31 + PC32 + PC33 + PC34 + PC35 +
## PC36 + PC37 + PC38 + PC39 + PC40 + PC41 + PC42 + PC43 + PC44 +
## PC45 + PC46 + PC47 + PC48 + PC49 + PC50 + PC51 + PC52 + PC53 +
## PC54 + PC55 + PC56 + PC57 + PC58 + PC59 + PC60 + PC61 + PC62 +
## PC63 + PC64 + PC65 + PC66 + PC67 + PC68 + PC69 + PC70 + PC71 +
## PC72 + PC73 + PC74 + PC75 + PC76 + PC77 + PC78 + PC79 + PC80 +
## PC81 + PC82 + PC83 + PC84 + PC85 + PC86 + PC87 + PC88 + PC89 +
## PC90 + PC91 + PC92 + PC93 + PC94 + PC95 + PC96 + PC97 + PC98 +
## PC99 + PC100 + PC101 + PC102 + PC103 + PC104 + PC105 + PC106 +
## PC107 + PC108 + PC109 + PC110 + PC111 + PC112 + PC113 + PC114 +
## PC115 + PC116 + PC117 + PC118 + PC119 + PC120 + PC121 + PC122 +
## PC123 + PC124 + PC125 + PC126 + PC127 + PC128 + PC129 + PC130 +
## PC131 + PC132 + PC133 + PC134 + PC135 + PC136 + PC137 + PC138 +
## PC139 + PC140 + PC141 + PC142 + PC143 + PC144 + PC145 + PC146 +
## PC147 + PC148 + PC149 + PC150 + PC151 + PC152 + PC153 + PC154 +
## PC155 + PC156 + PC157 + PC158 + PC159 + PC160 + PC161 + PC162 +
## PC163 + PC164print(grand.mean.formula)## y3.cuberoot ~ 1# Update feature.names because we may have transformed some features
feature.names = n[!n %in% label.names]Full Model
model.full = lm(formula , data.train)
summary(model.full)##
## Call:
## lm(formula = formula, data = data.train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.33559 -0.08715 -0.02338 0.06432 0.76105
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.001e+00 1.666e-03 3001.612 < 2e-16 ***
## PC1 -1.663e-03 1.446e-04 -11.506 < 2e-16 ***
## PC2 -3.578e-03 1.466e-04 -24.411 < 2e-16 ***
## PC3 -1.544e-03 1.469e-04 -10.511 < 2e-16 ***
## PC4 -1.223e-03 1.495e-04 -8.181 3.49e-16 ***
## PC5 7.730e-04 1.548e-04 4.992 6.15e-07 ***
## PC6 -4.598e-04 1.547e-04 -2.973 0.002961 **
## PC7 -7.426e-04 1.583e-04 -4.690 2.80e-06 ***
## PC8 -2.100e-04 1.603e-04 -1.310 0.190123
## PC9 -1.787e-04 1.655e-04 -1.080 0.280040
## PC10 -7.822e-05 1.678e-04 -0.466 0.641203
## PC11 -2.115e-03 1.803e-04 -11.734 < 2e-16 ***
## PC12 -1.758e-03 1.908e-04 -9.213 < 2e-16 ***
## PC13 1.148e-03 1.939e-04 5.923 3.35e-09 ***
## PC14 9.398e-04 2.005e-04 4.687 2.84e-06 ***
## PC15 -1.018e-04 2.040e-04 -0.499 0.617907
## PC16 1.339e-03 2.050e-04 6.531 7.13e-11 ***
## PC17 -7.998e-04 2.178e-04 -3.673 0.000242 ***
## PC18 -1.469e-03 2.274e-04 -6.460 1.14e-10 ***
## PC19 5.410e-05 2.275e-04 0.238 0.812015
## PC20 1.721e-03 2.500e-04 6.885 6.42e-12 ***
## PC21 2.477e-04 2.600e-04 0.952 0.340926
## PC22 5.364e-04 4.069e-04 1.318 0.187420
## PC23 1.301e-03 5.015e-04 2.594 0.009507 **
## PC24 -3.279e-03 5.897e-04 -5.561 2.81e-08 ***
## PC25 1.098e-03 6.577e-04 1.670 0.094941 .
## PC26 1.433e-03 6.767e-04 2.118 0.034233 *
## PC27 1.618e-03 6.810e-04 2.377 0.017497 *
## PC28 5.896e-04 6.919e-04 0.852 0.394178
## PC29 1.544e-03 7.568e-04 2.040 0.041401 *
## PC30 3.520e-04 7.711e-04 0.457 0.648001
## PC31 -9.859e-04 8.310e-04 -1.186 0.235497
## PC32 -2.748e-03 8.393e-04 -3.274 0.001068 **
## PC33 1.251e-03 8.585e-04 1.457 0.145139
## PC34 4.009e-03 9.073e-04 4.418 1.01e-05 ***
## PC35 2.322e-04 9.631e-04 0.241 0.809491
## PC36 -2.440e-04 9.771e-04 -0.250 0.802821
## PC37 -1.401e-03 1.016e-03 -1.379 0.167872
## PC38 1.095e-03 1.057e-03 1.036 0.300123
## PC39 -5.246e-04 1.073e-03 -0.489 0.624800
## PC40 -3.557e-04 1.078e-03 -0.330 0.741390
## PC41 2.163e-04 1.099e-03 0.197 0.844009
## PC42 1.854e-04 1.112e-03 0.167 0.867517
## PC43 2.383e-04 1.127e-03 0.211 0.832595
## PC44 1.721e-03 1.122e-03 1.534 0.125092
## PC45 -1.304e-03 1.124e-03 -1.160 0.246013
## PC46 2.240e-04 1.142e-03 0.196 0.844474
## PC47 -1.670e-03 1.149e-03 -1.454 0.146054
## PC48 1.224e-03 1.172e-03 1.045 0.296123
## PC49 1.122e-03 1.174e-03 0.956 0.339245
## PC50 -6.369e-04 1.183e-03 -0.538 0.590299
## PC51 7.903e-04 1.190e-03 0.664 0.506781
## PC52 1.773e-05 1.195e-03 0.015 0.988165
## PC53 2.587e-04 1.197e-03 0.216 0.828970
## PC54 -2.819e-04 1.205e-03 -0.234 0.815016
## PC55 -2.113e-04 1.206e-03 -0.175 0.860959
## PC56 6.500e-04 1.226e-03 0.530 0.595969
## PC57 -1.623e-03 1.234e-03 -1.315 0.188672
## PC58 8.245e-04 1.228e-03 0.672 0.501823
## PC59 2.455e-03 1.219e-03 2.013 0.044130 *
## PC60 -1.304e-03 1.245e-03 -1.047 0.295265
## PC61 1.976e-04 1.231e-03 0.160 0.872529
## PC62 -1.822e-04 1.256e-03 -0.145 0.884688
## PC63 -2.238e-03 1.255e-03 -1.783 0.074588 .
## PC64 -1.993e-03 1.261e-03 -1.581 0.114014
## PC65 -1.148e-03 1.257e-03 -0.913 0.361358
## PC66 -2.351e-03 1.275e-03 -1.844 0.065179 .
## PC67 -2.757e-04 1.287e-03 -0.214 0.830429
## PC68 2.589e-03 1.284e-03 2.017 0.043774 *
## PC69 1.592e-03 1.291e-03 1.233 0.217541
## PC70 -4.740e-04 1.297e-03 -0.365 0.714790
## PC71 2.825e-03 1.291e-03 2.187 0.028753 *
## PC72 7.206e-05 1.305e-03 0.055 0.955951
## PC73 7.575e-04 1.313e-03 0.577 0.564079
## PC74 -1.595e-03 1.318e-03 -1.210 0.226182
## PC75 -3.415e-03 1.325e-03 -2.578 0.009967 **
## PC76 3.557e-04 1.326e-03 0.268 0.788493
## PC77 1.765e-03 1.326e-03 1.331 0.183370
## PC78 1.473e-03 1.331e-03 1.106 0.268645
## PC79 2.454e-03 1.344e-03 1.825 0.067987 .
## PC80 -1.258e-03 1.367e-03 -0.920 0.357415
## PC81 3.799e-03 1.363e-03 2.788 0.005324 **
## PC82 6.021e-04 1.369e-03 0.440 0.660201
## PC83 -2.566e-03 1.360e-03 -1.886 0.059316 .
## PC84 3.514e-03 1.368e-03 2.568 0.010254 *
## PC85 4.670e-03 1.389e-03 3.363 0.000777 ***
## PC86 -2.149e-03 1.384e-03 -1.552 0.120711
## PC87 8.014e-03 1.402e-03 5.716 1.15e-08 ***
## PC88 -1.912e-03 1.422e-03 -1.344 0.178907
## PC89 -2.577e-03 1.398e-03 -1.843 0.065369 .
## PC90 -2.048e-03 1.405e-03 -1.458 0.144946
## PC91 -1.752e-04 1.411e-03 -0.124 0.901196
## PC92 -2.535e-04 1.423e-03 -0.178 0.858631
## PC93 -4.790e-04 1.408e-03 -0.340 0.733639
## PC94 -3.779e-03 1.418e-03 -2.665 0.007724 **
## PC95 -5.870e-04 1.430e-03 -0.411 0.681400
## PC96 -3.851e-03 1.438e-03 -2.677 0.007444 **
## PC97 -1.783e-03 1.430e-03 -1.246 0.212653
## PC98 -9.938e-04 1.436e-03 -0.692 0.489052
## PC99 -2.122e-03 1.437e-03 -1.476 0.139911
## PC100 -2.253e-04 1.436e-03 -0.157 0.875337
## PC101 -3.588e-04 1.435e-03 -0.250 0.802572
## PC102 -2.381e-03 1.457e-03 -1.634 0.102317
## PC103 2.814e-03 1.445e-03 1.948 0.051496 .
## PC104 -3.746e-03 1.451e-03 -2.581 0.009866 **
## PC105 2.963e-03 1.456e-03 2.035 0.041918 *
## PC106 3.630e-03 1.450e-03 2.504 0.012315 *
## PC107 1.162e-03 1.453e-03 0.800 0.423977
## PC108 2.455e-05 1.462e-03 0.017 0.986606
## PC109 2.111e-03 1.460e-03 1.446 0.148280
## PC110 -5.179e-04 1.455e-03 -0.356 0.721947
## PC111 -3.337e-03 1.470e-03 -2.270 0.023220 *
## PC112 -4.860e-04 1.470e-03 -0.331 0.740945
## PC113 1.610e-03 1.472e-03 1.093 0.274225
## PC114 -2.852e-03 1.469e-03 -1.941 0.052266 .
## PC115 -5.796e-03 1.480e-03 -3.917 9.08e-05 ***
## PC116 -6.925e-04 1.479e-03 -0.468 0.639695
## PC117 -2.214e-04 1.470e-03 -0.151 0.880275
## PC118 2.331e-03 1.486e-03 1.568 0.116913
## PC119 -2.920e-03 1.485e-03 -1.966 0.049317 *
## PC120 1.033e-03 1.483e-03 0.697 0.485922
## PC121 -1.211e-05 1.484e-03 -0.008 0.993489
## PC122 2.594e-03 1.494e-03 1.736 0.082572 .
## PC123 -2.418e-03 1.498e-03 -1.614 0.106511
## PC124 1.651e-03 1.501e-03 1.100 0.271557
## PC125 2.036e-03 1.506e-03 1.353 0.176270
## PC126 5.228e-04 1.492e-03 0.350 0.726015
## PC127 2.308e-03 1.489e-03 1.550 0.121148
## PC128 -1.919e-03 1.501e-03 -1.278 0.201285
## PC129 -1.535e-04 1.503e-03 -0.102 0.918649
## PC130 5.811e-04 1.516e-03 0.383 0.701498
## PC131 -3.983e-03 1.510e-03 -2.638 0.008357 **
## PC132 1.160e-03 1.509e-03 0.768 0.442299
## PC133 -1.385e-03 1.515e-03 -0.914 0.360657
## PC134 4.552e-03 1.504e-03 3.027 0.002478 **
## PC135 3.018e-03 1.510e-03 1.999 0.045683 *
## PC136 1.191e-03 1.526e-03 0.780 0.435280
## PC137 -8.056e-04 1.525e-03 -0.528 0.597326
## PC138 1.818e-03 1.530e-03 1.188 0.234897
## PC139 -3.505e-03 1.521e-03 -2.304 0.021268 *
## PC140 -1.269e-03 1.539e-03 -0.825 0.409519
## PC141 1.223e-05 1.534e-03 0.008 0.993642
## PC142 1.458e-05 1.539e-03 0.009 0.992443
## PC143 2.076e-03 1.538e-03 1.350 0.177153
## PC144 2.493e-03 1.535e-03 1.625 0.104270
## PC145 1.769e-03 1.541e-03 1.148 0.251143
## PC146 4.674e-03 1.547e-03 3.021 0.002530 **
## PC147 -9.552e-04 1.537e-03 -0.621 0.534354
## PC148 -2.039e-03 1.530e-03 -1.333 0.182750
## PC149 6.513e-04 1.553e-03 0.419 0.674907
## PC150 8.207e-04 1.550e-03 0.529 0.596518
## PC151 2.957e-03 1.556e-03 1.900 0.057473 .
## PC152 -4.070e-04 1.565e-03 -0.260 0.794780
## PC153 3.365e-03 1.550e-03 2.171 0.029948 *
## PC154 -3.574e-03 1.557e-03 -2.295 0.021747 *
## PC155 3.279e-03 1.559e-03 2.103 0.035469 *
## PC156 3.411e-03 1.564e-03 2.181 0.029194 *
## PC157 8.113e-04 1.568e-03 0.517 0.604866
## PC158 7.014e-04 1.567e-03 0.448 0.654499
## PC159 5.705e-03 1.559e-03 3.659 0.000255 ***
## PC160 9.694e-04 1.556e-03 0.623 0.533269
## PC161 1.538e-03 1.559e-03 0.986 0.324207
## PC162 -5.154e-03 1.579e-03 -3.265 0.001102 **
## PC163 2.629e-03 1.574e-03 1.670 0.094962 .
## PC164 5.116e-04 1.568e-03 0.326 0.744258
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1241 on 5419 degrees of freedom
## Multiple R-squared: 0.2498, Adjusted R-squared: 0.2271
## F-statistic: 11 on 164 and 5419 DF, p-value: < 2.2e-16cd.full = plot.diagnostics(model=model.full, train=data.train)
## [1] "Number of data points that have Cook's D > 4/n: 270"
## [1] "Number of data points that have Cook's D > 1: 0"Checking with removal of high influence points
high.cd = names(cd.full[cd.full > 4/nrow(data.train)])
#save dataset with high.cd flagged
t = data.train %>%
rownames_to_column() %>%
mutate(high.cd = ifelse(rowname %in% high.cd,1,0))
#write.csv(t,file='data_high_cd_flag.csv',row.names = F)
###
data.train2 = data.train[!(rownames(data.train)) %in% high.cd,]
model.full2 = lm(formula , data.train2)
summary(model.full2)##
## Call:
## lm(formula = formula, data = data.train2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.21882 -0.07427 -0.01502 0.06494 0.32144
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.987e+00 1.374e-03 3629.373 < 2e-16 ***
## PC1 -1.809e-03 1.218e-04 -14.848 < 2e-16 ***
## PC2 -3.501e-03 1.215e-04 -28.824 < 2e-16 ***
## PC3 -1.565e-03 1.224e-04 -12.792 < 2e-16 ***
## PC4 -1.386e-03 1.234e-04 -11.230 < 2e-16 ***
## PC5 7.595e-04 1.286e-04 5.907 3.70e-09 ***
## PC6 -3.108e-04 1.281e-04 -2.425 0.015330 *
## PC7 -7.746e-04 1.310e-04 -5.915 3.54e-09 ***
## PC8 -1.928e-04 1.332e-04 -1.448 0.147764
## PC9 -1.503e-05 1.373e-04 -0.109 0.912827
## PC10 2.024e-05 1.392e-04 0.145 0.884340
## PC11 -2.387e-03 1.488e-04 -16.040 < 2e-16 ***
## PC12 -1.838e-03 1.572e-04 -11.696 < 2e-16 ***
## PC13 1.124e-03 1.605e-04 7.001 2.87e-12 ***
## PC14 8.099e-04 1.654e-04 4.897 1.00e-06 ***
## PC15 -2.948e-04 1.691e-04 -1.743 0.081348 .
## PC16 1.194e-03 1.689e-04 7.067 1.79e-12 ***
## PC17 -8.941e-04 1.794e-04 -4.982 6.49e-07 ***
## PC18 -1.442e-03 1.871e-04 -7.705 1.56e-14 ***
## PC19 9.940e-05 1.886e-04 0.527 0.598125
## PC20 1.808e-03 2.067e-04 8.749 < 2e-16 ***
## PC21 2.458e-04 2.147e-04 1.145 0.252434
## PC22 7.010e-04 3.356e-04 2.089 0.036764 *
## PC23 1.443e-03 4.202e-04 3.433 0.000601 ***
## PC24 -3.477e-03 4.894e-04 -7.105 1.37e-12 ***
## PC25 1.354e-03 5.480e-04 2.471 0.013490 *
## PC26 7.814e-04 5.624e-04 1.389 0.164773
## PC27 1.204e-03 5.664e-04 2.126 0.033543 *
## PC28 1.645e-04 5.745e-04 0.286 0.774609
## PC29 1.517e-03 6.249e-04 2.428 0.015198 *
## PC30 4.725e-04 6.420e-04 0.736 0.461754
## PC31 -1.071e-03 6.916e-04 -1.549 0.121499
## PC32 -2.897e-03 6.954e-04 -4.166 3.16e-05 ***
## PC33 9.478e-05 7.179e-04 0.132 0.894967
## PC34 4.075e-03 7.486e-04 5.444 5.45e-08 ***
## PC35 4.622e-04 8.049e-04 0.574 0.565869
## PC36 -1.101e-03 8.141e-04 -1.352 0.176441
## PC37 -1.679e-03 8.415e-04 -1.996 0.046031 *
## PC38 1.381e-03 8.742e-04 1.580 0.114220
## PC39 -3.493e-05 9.325e-04 -0.037 0.970122
## PC40 -3.500e-04 9.024e-04 -0.388 0.698116
## PC41 -4.850e-04 9.136e-04 -0.531 0.595545
## PC42 1.448e-03 9.301e-04 1.557 0.119454
## PC43 9.782e-04 9.487e-04 1.031 0.302568
## PC44 6.531e-04 9.541e-04 0.685 0.493663
## PC45 -1.243e-03 9.428e-04 -1.319 0.187379
## PC46 2.784e-04 9.507e-04 0.293 0.769670
## PC47 -1.762e-03 9.627e-04 -1.830 0.067288 .
## PC48 9.954e-04 9.743e-04 1.022 0.306986
## PC49 2.300e-03 9.834e-04 2.338 0.019407 *
## PC50 -1.327e-03 9.956e-04 -1.333 0.182568
## PC51 1.178e-03 1.003e-03 1.174 0.240539
## PC52 -3.593e-04 9.989e-04 -0.360 0.719063
## PC53 1.665e-03 9.962e-04 1.672 0.094615 .
## PC54 -6.463e-04 1.014e-03 -0.638 0.523801
## PC55 -1.977e-03 1.012e-03 -1.953 0.050902 .
## PC56 3.395e-04 1.030e-03 0.330 0.741771
## PC57 -2.451e-03 1.026e-03 -2.389 0.016943 *
## PC58 -1.341e-03 1.030e-03 -1.302 0.193055
## PC59 2.614e-03 1.024e-03 2.552 0.010736 *
## PC60 -1.879e-03 1.042e-03 -1.803 0.071460 .
## PC61 -5.407e-04 1.025e-03 -0.528 0.597735
## PC62 6.312e-04 1.054e-03 0.599 0.549249
## PC63 -2.096e-03 1.052e-03 -1.992 0.046431 *
## PC64 -1.793e-03 1.052e-03 -1.705 0.088246 .
## PC65 -1.661e-03 1.052e-03 -1.578 0.114614
## PC66 -1.570e-03 1.071e-03 -1.466 0.142662
## PC67 -1.365e-04 1.076e-03 -0.127 0.899076
## PC68 1.919e-03 1.074e-03 1.787 0.073964 .
## PC69 2.473e-03 1.085e-03 2.279 0.022718 *
## PC70 3.574e-04 1.077e-03 0.332 0.740126
## PC71 2.018e-03 1.073e-03 1.881 0.060040 .
## PC72 -1.189e-04 1.084e-03 -0.110 0.912685
## PC73 1.102e-03 1.094e-03 1.008 0.313655
## PC74 -5.347e-05 1.101e-03 -0.049 0.961255
## PC75 -2.533e-03 1.106e-03 -2.290 0.022038 *
## PC76 -4.901e-04 1.099e-03 -0.446 0.655659
## PC77 1.877e-03 1.101e-03 1.704 0.088400 .
## PC78 -9.855e-05 1.107e-03 -0.089 0.929098
## PC79 3.123e-03 1.118e-03 2.795 0.005214 **
## PC80 -7.226e-04 1.129e-03 -0.640 0.522150
## PC81 4.163e-03 1.128e-03 3.689 0.000227 ***
## PC82 2.091e-04 1.136e-03 0.184 0.853915
## PC83 -2.914e-03 1.136e-03 -2.565 0.010355 *
## PC84 3.204e-03 1.136e-03 2.820 0.004819 **
## PC85 5.224e-03 1.160e-03 4.505 6.79e-06 ***
## PC86 -7.154e-04 1.148e-03 -0.623 0.533092
## PC87 7.390e-03 1.162e-03 6.361 2.17e-10 ***
## PC88 -1.939e-03 1.181e-03 -1.643 0.100507
## PC89 -2.070e-03 1.159e-03 -1.785 0.074296 .
## PC90 -1.476e-03 1.169e-03 -1.263 0.206738
## PC91 7.141e-05 1.163e-03 0.061 0.951027
## PC92 9.746e-04 1.173e-03 0.831 0.406269
## PC93 -1.545e-03 1.168e-03 -1.322 0.186179
## PC94 -2.938e-03 1.173e-03 -2.503 0.012329 *
## PC95 -1.976e-04 1.186e-03 -0.167 0.867716
## PC96 -3.359e-03 1.188e-03 -2.828 0.004709 **
## PC97 -1.164e-03 1.185e-03 -0.982 0.326024
## PC98 -6.647e-04 1.189e-03 -0.559 0.576069
## PC99 -6.694e-04 1.194e-03 -0.561 0.575057
## PC100 -9.248e-04 1.182e-03 -0.783 0.433896
## PC101 -1.182e-03 1.188e-03 -0.995 0.319678
## PC102 -1.700e-03 1.206e-03 -1.410 0.158568
## PC103 2.440e-03 1.196e-03 2.040 0.041400 *
## PC104 -3.327e-03 1.197e-03 -2.779 0.005464 **
## PC105 2.911e-03 1.208e-03 2.409 0.016010 *
## PC106 3.239e-03 1.197e-03 2.706 0.006838 **
## PC107 1.382e-03 1.210e-03 1.142 0.253523
## PC108 -8.645e-04 1.209e-03 -0.715 0.474654
## PC109 1.722e-03 1.207e-03 1.426 0.153872
## PC110 -4.221e-04 1.202e-03 -0.351 0.725557
## PC111 -3.743e-03 1.218e-03 -3.074 0.002121 **
## PC112 -4.776e-04 1.215e-03 -0.393 0.694299
## PC113 1.859e-03 1.214e-03 1.531 0.125723
## PC114 -2.621e-03 1.214e-03 -2.159 0.030930 *
## PC115 -6.776e-03 1.223e-03 -5.540 3.17e-08 ***
## PC116 -1.748e-04 1.222e-03 -0.143 0.886254
## PC117 4.638e-04 1.215e-03 0.382 0.702773
## PC118 7.335e-04 1.227e-03 0.598 0.550098
## PC119 -2.160e-03 1.226e-03 -1.762 0.078197 .
## PC120 1.097e-03 1.228e-03 0.893 0.371752
## PC121 -1.600e-03 1.223e-03 -1.308 0.190982
## PC122 2.408e-03 1.234e-03 1.951 0.051071 .
## PC123 -1.912e-03 1.237e-03 -1.545 0.122343
## PC124 2.971e-04 1.244e-03 0.239 0.811165
## PC125 2.970e-03 1.242e-03 2.391 0.016821 *
## PC126 7.033e-04 1.234e-03 0.570 0.568623
## PC127 1.276e-03 1.230e-03 1.037 0.299691
## PC128 -2.061e-03 1.238e-03 -1.665 0.095898 .
## PC129 -1.659e-04 1.249e-03 -0.133 0.894302
## PC130 5.294e-04 1.253e-03 0.423 0.672555
## PC131 -3.047e-03 1.245e-03 -2.447 0.014443 *
## PC132 3.191e-04 1.250e-03 0.255 0.798434
## PC133 -1.188e-03 1.262e-03 -0.941 0.346660
## PC134 2.908e-03 1.243e-03 2.340 0.019306 *
## PC135 1.695e-03 1.247e-03 1.360 0.174042
## PC136 1.668e-03 1.266e-03 1.318 0.187609
## PC137 -1.638e-03 1.258e-03 -1.302 0.192921
## PC138 1.992e-03 1.269e-03 1.570 0.116538
## PC139 -2.933e-03 1.260e-03 -2.328 0.019936 *
## PC140 -1.559e-03 1.271e-03 -1.226 0.220256
## PC141 1.003e-03 1.270e-03 0.790 0.429429
## PC142 1.327e-03 1.271e-03 1.045 0.296258
## PC143 1.950e-03 1.270e-03 1.536 0.124609
## PC144 1.772e-03 1.271e-03 1.394 0.163457
## PC145 3.087e-03 1.277e-03 2.418 0.015639 *
## PC146 5.987e-03 1.274e-03 4.698 2.70e-06 ***
## PC147 -1.116e-03 1.275e-03 -0.875 0.381405
## PC148 -1.835e-03 1.261e-03 -1.455 0.145785
## PC149 7.123e-05 1.280e-03 0.056 0.955640
## PC150 1.585e-03 1.284e-03 1.235 0.216894
## PC151 2.715e-03 1.282e-03 2.119 0.034179 *
## PC152 -5.475e-04 1.295e-03 -0.423 0.672471
## PC153 2.200e-03 1.277e-03 1.722 0.085101 .
## PC154 -2.471e-03 1.291e-03 -1.915 0.055561 .
## PC155 2.414e-03 1.283e-03 1.882 0.059949 .
## PC156 1.955e-03 1.294e-03 1.511 0.130768
## PC157 1.366e-03 1.298e-03 1.053 0.292529
## PC158 6.729e-04 1.301e-03 0.517 0.604969
## PC159 4.557e-03 1.284e-03 3.549 0.000391 ***
## PC160 5.971e-04 1.296e-03 0.461 0.645090
## PC161 -6.825e-04 1.288e-03 -0.530 0.596279
## PC162 -6.019e-03 1.303e-03 -4.620 3.94e-06 ***
## PC163 2.291e-03 1.307e-03 1.754 0.079558 .
## PC164 4.710e-04 1.295e-03 0.364 0.716096
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.09981 on 5149 degrees of freedom
## Multiple R-squared: 0.3423, Adjusted R-squared: 0.3213
## F-statistic: 16.34 on 164 and 5149 DF, p-value: < 2.2e-16cd.full2 = plot.diagnostics(model.full2, data.train2)
## [1] "Number of data points that have Cook's D > 4/n: 240"
## [1] "Number of data points that have Cook's D > 1: 0"# much more normal residuals than before.
# Checking to see if distributions are different and if so whcih variables
# High Leverage Plot
plotData = data.train %>%
rownames_to_column() %>%
mutate(type=ifelse(rowname %in% high.cd,'High','Normal')) %>%
dplyr::select(type,target=one_of(label.names))
ggplot(data=plotData, aes(x=type,y=target)) +
geom_boxplot(fill='light blue',outlier.shape=NA) +
scale_y_continuous(name="Target Variable Values",label=scales::comma_format(accuracy=.1)) +
theme_light() +
ggtitle('Distribution of High Leverage Points and Normal Points')
# 2 sample t-tests
plotData = data.train %>%
rownames_to_column() %>%
mutate(type=ifelse(rowname %in% high.cd,'High','Normal')) %>%
dplyr::select(type,one_of(feature.names))
comp.test = lapply(dplyr::select(plotData, one_of(feature.names))
, function(x) t.test(x ~ plotData$type, var.equal = TRUE))
sig.comp = list.filter(comp.test, p.value < 0.05)
sapply(sig.comp, function(x) x[['p.value']])## PC1 PC6 PC11 PC23 PC25 PC26 PC28 PC33 PC39
## 1.858533e-06 3.464657e-02 7.293096e-04 4.145808e-05 1.038696e-03 3.260100e-04 2.978237e-02 2.013420e-02 1.440239e-02
## PC44 PC45 PC55 PC75 PC78 PC87 PC124 PC134 PC159
## 1.095256e-02 8.523271e-04 2.904629e-02 3.300027e-02 2.014597e-02 3.646907e-02 4.622152e-02 2.571908e-02 3.677550e-02
## PC161
## 1.455333e-02mm = melt(plotData, id=c('type')) %>% filter(variable %in% names(sig.comp))
ggplot(mm,aes(x=type, y=value)) +
geom_boxplot()+
facet_wrap(~variable, ncol=5, scales = 'free_y') +
scale_y_continuous(name="values",label=scales::comma_format(accuracy=.1)) +
ggtitle('Distribution of High Leverage Points and Normal Points')
# Distribution (box) Plots
mm = melt(plotData, id=c('type'))
ggplot(mm,aes(x=type, y=value)) +
geom_boxplot()+
facet_wrap(~variable, ncol=8, scales = 'free_y') +
scale_y_continuous(name="values",label=scales::comma_format(accuracy=.1)) +
ggtitle('Distribution of High Leverage Points and Normal Points')
Grand Means Model
model.null = lm(grand.mean.formula, data.train)
summary(model.null)##
## Call:
## lm(formula = grand.mean.formula, data = data.train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.42417 -0.09356 -0.01542 0.07840 0.78460
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.001635 0.001889 2647 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1412 on 5583 degrees of freedomVariable Selection
Basic: http://www.stat.columbia.edu/~martin/W2024/R10.pdf Cross Validation + Other Metrics: http://www.sthda.com/english/articles/37-model-selection-essentials-in-r/154-stepwise-regression-essentials-in-r/
Forward Selection with CV
Train
if (algo.forward.caret == TRUE){
set.seed(1)
returned = train.caret.glmselect(formula = formula
, data = data.train
, method = "leapForward"
, feature.names = feature.names)
model.forward = returned$model
id = returned$id
}## Aggregating results
## Selecting tuning parameters
## Fitting nvmax = 105 on full training set
## [1] "All models results"
## nvmax RMSE Rsquared MAE RMSESD RsquaredSD MAESD
## 1 1 0.1350468 0.08479660 0.10436184 0.005200049 0.01674113 0.002954202
## 2 2 0.1339628 0.09935862 0.10371363 0.005504447 0.01832821 0.003125743
## 3 3 0.1323635 0.12089088 0.10239954 0.005815779 0.02088009 0.003384538
## 4 4 0.1318132 0.12800310 0.10189097 0.005452716 0.01669327 0.003230049
## 5 5 0.1304285 0.14641271 0.10072021 0.005540135 0.01964057 0.003224118
## 6 6 0.1297260 0.15545312 0.10010572 0.005332458 0.01959561 0.002999176
## 7 7 0.1296458 0.15676998 0.10011934 0.005408872 0.01921091 0.003198788
## 8 8 0.1292860 0.16166820 0.09983246 0.005666917 0.02223766 0.003270292
## 9 9 0.1288372 0.16765598 0.09957128 0.005687598 0.02264859 0.003320170
## 10 10 0.1283193 0.17429662 0.09917594 0.005966020 0.02433558 0.003541938
## 11 11 0.1279362 0.17921957 0.09888127 0.005983356 0.02473557 0.003442295
## 12 12 0.1276569 0.18260370 0.09866195 0.005781548 0.02152010 0.003269757
## 13 13 0.1272739 0.18759117 0.09845644 0.005768872 0.02351046 0.003179434
## 14 14 0.1271615 0.18912503 0.09835234 0.005751381 0.02366383 0.003130328
## 15 15 0.1268642 0.19307028 0.09806442 0.005948943 0.02602667 0.003223252
## 16 16 0.1266694 0.19544374 0.09789322 0.005856941 0.02430375 0.003202948
## 17 17 0.1264706 0.19794585 0.09769118 0.005836174 0.02458856 0.003211562
## 18 18 0.1264844 0.19784441 0.09761652 0.005839495 0.02497885 0.003228483
## 19 19 0.1264275 0.19857322 0.09763926 0.005815373 0.02587255 0.003356488
## 20 20 0.1263052 0.20012438 0.09754751 0.005853704 0.02690377 0.003357624
## 21 21 0.1263884 0.19900583 0.09752871 0.005791377 0.02509730 0.003267652
## 22 22 0.1263051 0.20012161 0.09751512 0.005871821 0.02659607 0.003378924
## 23 23 0.1263833 0.19920885 0.09756776 0.005879425 0.02633925 0.003369958
## 24 24 0.1264223 0.19868676 0.09764942 0.005783628 0.02439144 0.003254422
## 25 25 0.1265097 0.19760003 0.09770993 0.005654214 0.02347045 0.003139757
## 26 26 0.1263927 0.19910993 0.09762567 0.005763593 0.02351943 0.003075068
## 27 27 0.1263814 0.19939537 0.09763183 0.005665547 0.02346896 0.003028282
## 28 28 0.1264759 0.19825074 0.09773256 0.005612793 0.02317772 0.002975545
## 29 29 0.1265454 0.19753824 0.09779892 0.005725031 0.02481153 0.003079489
## 30 30 0.1265390 0.19769106 0.09782618 0.005719897 0.02490035 0.003116986
## 31 31 0.1265541 0.19751539 0.09775613 0.005613531 0.02382063 0.003060166
## 32 32 0.1265618 0.19748093 0.09775847 0.005632815 0.02439437 0.003037837
## 33 33 0.1266044 0.19708571 0.09776977 0.005623306 0.02367647 0.002977068
## 34 34 0.1266824 0.19630060 0.09779546 0.005561872 0.02369771 0.002961893
## 35 35 0.1267466 0.19550167 0.09788808 0.005532787 0.02223223 0.002938956
## 36 36 0.1267695 0.19528058 0.09793055 0.005501084 0.02251962 0.002907074
## 37 37 0.1267451 0.19557827 0.09790324 0.005454463 0.02223763 0.002888294
## 38 38 0.1267693 0.19534713 0.09797083 0.005391634 0.02254449 0.002786412
## 39 39 0.1266653 0.19656588 0.09788934 0.005448440 0.02266691 0.002864593
## 40 40 0.1266227 0.19715789 0.09789099 0.005471754 0.02366100 0.002851723
## 41 41 0.1266599 0.19673873 0.09790957 0.005442954 0.02262700 0.002774776
## 42 42 0.1266683 0.19672580 0.09792747 0.005549211 0.02294082 0.002831955
## 43 43 0.1266416 0.19709099 0.09790827 0.005505759 0.02267340 0.002819348
## 44 44 0.1266086 0.19739575 0.09790638 0.005416161 0.02188588 0.002757002
## 45 45 0.1265564 0.19808013 0.09787427 0.005384404 0.02171558 0.002700684
## 46 46 0.1265033 0.19873246 0.09783729 0.005437616 0.02215195 0.002743259
## 47 47 0.1264629 0.19926641 0.09778888 0.005404469 0.02336698 0.002781684
## 48 48 0.1264402 0.19963053 0.09776667 0.005427534 0.02371584 0.002847824
## 49 49 0.1264640 0.19934378 0.09777062 0.005452431 0.02407712 0.002890590
## 50 50 0.1265739 0.19815080 0.09789846 0.005471787 0.02397588 0.002942941
## 51 51 0.1265812 0.19812751 0.09789149 0.005435745 0.02455158 0.002918752
## 52 52 0.1265963 0.19808387 0.09790489 0.005474396 0.02586658 0.002915236
## 53 53 0.1265387 0.19880186 0.09781448 0.005522736 0.02669581 0.002978187
## 54 54 0.1264480 0.19991283 0.09779467 0.005474579 0.02633216 0.002956309
## 55 55 0.1264945 0.19946218 0.09779117 0.005562932 0.02600976 0.003009604
## 56 56 0.1265335 0.19903781 0.09777038 0.005640060 0.02620808 0.003049090
## 57 57 0.1264780 0.19967890 0.09774572 0.005622726 0.02576035 0.003065567
## 58 58 0.1263953 0.20068770 0.09767922 0.005641043 0.02619692 0.003118879
## 59 59 0.1263521 0.20121414 0.09763178 0.005575344 0.02568152 0.003113462
## 60 60 0.1263945 0.20070174 0.09763835 0.005529801 0.02507800 0.003095519
## 61 61 0.1264187 0.20041309 0.09764587 0.005479315 0.02500401 0.003073573
## 62 62 0.1264141 0.20045683 0.09765546 0.005456674 0.02474086 0.003041280
## 63 63 0.1263678 0.20100727 0.09758721 0.005456709 0.02479016 0.003053931
## 64 64 0.1264259 0.20031310 0.09763725 0.005424525 0.02429027 0.003013452
## 65 65 0.1263915 0.20074182 0.09762058 0.005474633 0.02472960 0.003067736
## 66 66 0.1263666 0.20102402 0.09763115 0.005459813 0.02481906 0.003069059
## 67 67 0.1263352 0.20143800 0.09762473 0.005419271 0.02429941 0.003044765
## 68 68 0.1263604 0.20111577 0.09767420 0.005388026 0.02386378 0.003004040
## 69 69 0.1263256 0.20149491 0.09766525 0.005393875 0.02350204 0.003042984
## 70 70 0.1263191 0.20158462 0.09768275 0.005388450 0.02318230 0.003041991
## 71 71 0.1263319 0.20152204 0.09765607 0.005424528 0.02345475 0.003059108
## 72 72 0.1263507 0.20134278 0.09765753 0.005409843 0.02326292 0.003029063
## 73 73 0.1263127 0.20174794 0.09764753 0.005408784 0.02371303 0.003030095
## 74 74 0.1262823 0.20213249 0.09763507 0.005380452 0.02341940 0.003051790
## 75 75 0.1262955 0.20193889 0.09764842 0.005294301 0.02208380 0.003008360
## 76 76 0.1262576 0.20237163 0.09760968 0.005285759 0.02153622 0.002943634
## 77 77 0.1262600 0.20238827 0.09764030 0.005304007 0.02217754 0.002983743
## 78 78 0.1262513 0.20249432 0.09765677 0.005316849 0.02183534 0.002975682
## 79 79 0.1262544 0.20250739 0.09764341 0.005361154 0.02205173 0.003021316
## 80 80 0.1262282 0.20283190 0.09760474 0.005351637 0.02188648 0.003037540
## 81 81 0.1261947 0.20320912 0.09756195 0.005370144 0.02142310 0.003045244
## 82 82 0.1262093 0.20305084 0.09757602 0.005407741 0.02185420 0.003112448
## 83 83 0.1261835 0.20338392 0.09755670 0.005398219 0.02174522 0.003121264
## 84 84 0.1261907 0.20334297 0.09754375 0.005393609 0.02151949 0.003151462
## 85 85 0.1261944 0.20333682 0.09751809 0.005375952 0.02196709 0.003147737
## 86 86 0.1262177 0.20304697 0.09752040 0.005390500 0.02250195 0.003188625
## 87 87 0.1262038 0.20328214 0.09750174 0.005386450 0.02294063 0.003212902
## 88 88 0.1262078 0.20322895 0.09749956 0.005371534 0.02238164 0.003149563
## 89 89 0.1261955 0.20335164 0.09746301 0.005393621 0.02259959 0.003139729
## 90 90 0.1262031 0.20327162 0.09747814 0.005369308 0.02265144 0.003124153
## 91 91 0.1262115 0.20318239 0.09747607 0.005327149 0.02229746 0.003105752
## 92 92 0.1261785 0.20358110 0.09743758 0.005340240 0.02258254 0.003133814
## 93 93 0.1261453 0.20398661 0.09740363 0.005350952 0.02287706 0.003111678
## 94 94 0.1260985 0.20453063 0.09737577 0.005314660 0.02309334 0.003073066
## 95 95 0.1261075 0.20443558 0.09738597 0.005357368 0.02297656 0.003099529
## 96 96 0.1260961 0.20457613 0.09738752 0.005369947 0.02294345 0.003079345
## 97 97 0.1260800 0.20479082 0.09739708 0.005360230 0.02250364 0.003048303
## 98 98 0.1260107 0.20557862 0.09733183 0.005379360 0.02215388 0.003057055
## 99 99 0.1259765 0.20597782 0.09730535 0.005412239 0.02246005 0.003091609
## 100 100 0.1259431 0.20637870 0.09728196 0.005414094 0.02208661 0.003088996
## 101 101 0.1259543 0.20627339 0.09729632 0.005403693 0.02176376 0.003094779
## 102 102 0.1259519 0.20631170 0.09729305 0.005411918 0.02220200 0.003113944
## 103 103 0.1259435 0.20641424 0.09729648 0.005423045 0.02270903 0.003152905
## 104 104 0.1259293 0.20662362 0.09729779 0.005443799 0.02288207 0.003176505
## 105 105 0.1259052 0.20691319 0.09728686 0.005450328 0.02273456 0.003193748
## 106 106 0.1259107 0.20687083 0.09728522 0.005454628 0.02284862 0.003198774
## 107 107 0.1259421 0.20653396 0.09731947 0.005455741 0.02303401 0.003209778
## 108 108 0.1259642 0.20628464 0.09733366 0.005451393 0.02285053 0.003210432
## 109 109 0.1259634 0.20631324 0.09732236 0.005428053 0.02250955 0.003172108
## 110 110 0.1259679 0.20631675 0.09732433 0.005452312 0.02253926 0.003188762
## 111 111 0.1259710 0.20628299 0.09731483 0.005405769 0.02232346 0.003160585
## 112 112 0.1259680 0.20629315 0.09730748 0.005372698 0.02230929 0.003141726
## 113 113 0.1259777 0.20620584 0.09727584 0.005390408 0.02245424 0.003154222
## 114 114 0.1259837 0.20610423 0.09727649 0.005382296 0.02224748 0.003164201
## 115 115 0.1259927 0.20600764 0.09729254 0.005369456 0.02205479 0.003167334
## 116 116 0.1260079 0.20583256 0.09731536 0.005373486 0.02195621 0.003168683
## 117 117 0.1260436 0.20544271 0.09734919 0.005381737 0.02214890 0.003172554
## 118 118 0.1260755 0.20509228 0.09737181 0.005379707 0.02229585 0.003181631
## 119 119 0.1260912 0.20491679 0.09738780 0.005389848 0.02222420 0.003183516
## 120 120 0.1260932 0.20491415 0.09739337 0.005377898 0.02206991 0.003183617
## 121 121 0.1261103 0.20473485 0.09741187 0.005383653 0.02215728 0.003184888
## 122 122 0.1261143 0.20470180 0.09741450 0.005400070 0.02232558 0.003205105
## 123 123 0.1261168 0.20467904 0.09742284 0.005400710 0.02235790 0.003202254
## 124 124 0.1261518 0.20429543 0.09745291 0.005401608 0.02242096 0.003192159
## 125 125 0.1261578 0.20424997 0.09746621 0.005426437 0.02270965 0.003225716
## 126 126 0.1261498 0.20435044 0.09746041 0.005430491 0.02253847 0.003242284
## 127 127 0.1261696 0.20413922 0.09746916 0.005456752 0.02279187 0.003256842
## 128 128 0.1261829 0.20399744 0.09748504 0.005445996 0.02260785 0.003246411
## 129 129 0.1261897 0.20392713 0.09748183 0.005438888 0.02250361 0.003248616
## 130 130 0.1261895 0.20393660 0.09748744 0.005443065 0.02266185 0.003250012
## 131 131 0.1261799 0.20405202 0.09748314 0.005456300 0.02277028 0.003249011
## 132 132 0.1261836 0.20401152 0.09748293 0.005452311 0.02268762 0.003255315
## 133 133 0.1261815 0.20401891 0.09747862 0.005445579 0.02247635 0.003247413
## 134 134 0.1261903 0.20392632 0.09748109 0.005431535 0.02239767 0.003242716
## 135 135 0.1262091 0.20372009 0.09749865 0.005434270 0.02239300 0.003260230
## 136 136 0.1261984 0.20383965 0.09748288 0.005457746 0.02252193 0.003274988
## 137 137 0.1261996 0.20384482 0.09748329 0.005463124 0.02247554 0.003277424
## 138 138 0.1261933 0.20390311 0.09748450 0.005451886 0.02239290 0.003265183
## 139 139 0.1261872 0.20397997 0.09748649 0.005445918 0.02238028 0.003259647
## 140 140 0.1262145 0.20367801 0.09750743 0.005445322 0.02224547 0.003260391
## 141 141 0.1262132 0.20368643 0.09749754 0.005442087 0.02210782 0.003254281
## 142 142 0.1262146 0.20367262 0.09750135 0.005437216 0.02215196 0.003248653
## 143 143 0.1262096 0.20372876 0.09750517 0.005438812 0.02213515 0.003254118
## 144 144 0.1262141 0.20367935 0.09750982 0.005435561 0.02206687 0.003248656
## 145 145 0.1262060 0.20376658 0.09750987 0.005442310 0.02209094 0.003254436
## 146 146 0.1262051 0.20377735 0.09750987 0.005451347 0.02213734 0.003253233
## 147 147 0.1262041 0.20378497 0.09751183 0.005461005 0.02219693 0.003258773
## 148 148 0.1261995 0.20384308 0.09751107 0.005465376 0.02218786 0.003265796
## 149 149 0.1262044 0.20378893 0.09751134 0.005468523 0.02218228 0.003262595
## 150 150 0.1262027 0.20381211 0.09750763 0.005468089 0.02217296 0.003261503
## 151 151 0.1262090 0.20373619 0.09751575 0.005460952 0.02209842 0.003255790
## 152 152 0.1262037 0.20378890 0.09751525 0.005462154 0.02208358 0.003251597
## 153 153 0.1262071 0.20375273 0.09752227 0.005465137 0.02207422 0.003253257
## 154 154 0.1262073 0.20375241 0.09752350 0.005463187 0.02208191 0.003250070
## 155 155 0.1262034 0.20380067 0.09752149 0.005463287 0.02209506 0.003248892
## 156 156 0.1262023 0.20381833 0.09751753 0.005464455 0.02209686 0.003251020
## 157 157 0.1262058 0.20377730 0.09752006 0.005464224 0.02208234 0.003250305
## 158 158 0.1262066 0.20376829 0.09752177 0.005461336 0.02206925 0.003248812
## 159 159 0.1262076 0.20375611 0.09752366 0.005460250 0.02206564 0.003248059
## 160 160 0.1262103 0.20372445 0.09752663 0.005458698 0.02202558 0.003245804
## 161 161 0.1262111 0.20371422 0.09752690 0.005459543 0.02202359 0.003246306
## 162 162 0.1262102 0.20372134 0.09752614 0.005458645 0.02202366 0.003245864
## 163 163 0.1262109 0.20371360 0.09752644 0.005459111 0.02202303 0.003246147
## 164 164 0.1262107 0.20371699 0.09752633 0.005459230 0.02202556 0.003246293
## [1] "Best Model"
## nvmax
## 105 105
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## [1] "Coefficients of final model:"
## Estimate 2.5 % 97.5 %
## (Intercept) 5.0014260845 4.998178e+00 5.004674e+00
## PC1 -0.0016578295 -1.939429e-03 -1.376230e-03
## PC2 -0.0035750955 -3.860737e-03 -3.289454e-03
## PC3 -0.0015501926 -1.836532e-03 -1.263853e-03
## PC4 -0.0012180774 -1.509401e-03 -9.267541e-04
## PC5 0.0007735608 4.718221e-04 1.075300e-03
## PC6 -0.0004595017 -7.609634e-04 -1.580401e-04
## PC7 -0.0007431548 -1.051640e-03 -4.346692e-04
## PC8 -0.0002118816 -5.243793e-04 1.006161e-04
## PC9 -0.0001761755 -4.985975e-04 1.462465e-04
## PC11 -0.0021135209 -2.464943e-03 -1.762099e-03
## PC12 -0.0017536810 -2.125771e-03 -1.381591e-03
## PC13 0.0011491789 7.712343e-04 1.527123e-03
## PC14 0.0009467031 5.559444e-04 1.337462e-03
## PC16 0.0013417027 9.419079e-04 1.741498e-03
## PC17 -0.0008029682 -1.227550e-03 -3.783867e-04
## PC18 -0.0014706461 -1.913809e-03 -1.027483e-03
## PC20 0.0017173999 1.229914e-03 2.204886e-03
## PC21 0.0002436889 -2.633654e-04 7.507433e-04
## PC22 0.0005313850 -2.621268e-04 1.324897e-03
## PC23 0.0012901432 3.129468e-04 2.267340e-03
## PC24 -0.0032796404 -4.428912e-03 -2.130369e-03
## PC25 0.0011063330 -1.757167e-04 2.388383e-03
## PC26 0.0014168399 9.744754e-05 2.736232e-03
## PC27 0.0015982836 2.710758e-04 2.925491e-03
## PC28 0.0006027089 -7.458642e-04 1.951282e-03
## PC29 0.0015286200 5.311022e-05 3.004130e-03
## PC31 -0.0009951147 -2.614946e-03 6.247170e-04
## PC32 -0.0027512834 -4.387171e-03 -1.115396e-03
## PC33 0.0012921149 -3.804795e-04 2.964709e-03
## PC34 0.0040388349 2.271057e-03 5.806613e-03
## PC37 -0.0013890918 -3.368627e-03 5.904436e-04
## PC38 0.0011074596 -9.527628e-04 3.167682e-03
## PC44 0.0017152667 -4.707702e-04 3.901304e-03
## PC45 -0.0013005600 -3.489601e-03 8.884812e-04
## PC47 -0.0015957827 -3.833214e-03 6.416481e-04
## PC48 0.0012556465 -1.026536e-03 3.537829e-03
## PC49 0.0011123770 -1.175229e-03 3.399983e-03
## PC57 -0.0016637368 -4.069017e-03 7.415431e-04
## PC59 0.0024513197 7.462271e-05 4.828017e-03
## PC60 -0.0013234917 -3.749661e-03 1.102678e-03
## PC63 -0.0021920542 -4.637903e-03 2.537943e-04
## PC64 -0.0019720970 -4.428624e-03 4.844301e-04
## PC65 -0.0011485676 -3.599165e-03 1.302029e-03
## PC66 -0.0023344523 -4.817857e-03 1.489525e-04
## PC68 0.0026013386 9.894665e-05 5.103731e-03
## PC69 0.0016019835 -9.139311e-04 4.117898e-03
## PC71 0.0028849599 3.688310e-04 5.401089e-03
## PC74 -0.0016045929 -4.171966e-03 9.627805e-04
## PC75 -0.0034056174 -5.987307e-03 -8.239278e-04
## PC77 0.0017444035 -8.409127e-04 4.329720e-03
## PC78 0.0014906992 -1.104279e-03 4.085678e-03
## PC79 0.0024646909 -1.554206e-04 5.084802e-03
## PC80 -0.0012272159 -3.891748e-03 1.437317e-03
## PC81 0.0038008121 1.145317e-03 6.456307e-03
## PC83 -0.0025461363 -5.197721e-03 1.054481e-04
## PC84 0.0034510898 7.845560e-04 6.117624e-03
## PC85 0.0046356082 1.929448e-03 7.341768e-03
## PC86 -0.0021140182 -4.813685e-03 5.856487e-04
## PC87 0.0079917487 5.259955e-03 1.072354e-02
## PC88 -0.0019045359 -4.675823e-03 8.667510e-04
## PC89 -0.0025765316 -5.301423e-03 1.483598e-04
## PC90 -0.0019874258 -4.724691e-03 7.498397e-04
## PC94 -0.0037782715 -6.542931e-03 -1.013612e-03
## PC96 -0.0038403925 -6.644133e-03 -1.036652e-03
## PC97 -0.0018094836 -4.596880e-03 9.779123e-04
## PC99 -0.0021723584 -4.974145e-03 6.294277e-04
## PC102 -0.0024153961 -5.255351e-03 4.245584e-04
## PC103 0.0028025654 -1.507000e-05 5.620201e-03
## PC104 -0.0037283368 -6.556930e-03 -8.997441e-04
## PC105 0.0030271855 1.888463e-04 5.865525e-03
## PC106 0.0036465850 8.213900e-04 6.471780e-03
## PC107 0.0012164069 -1.615229e-03 4.048043e-03
## PC109 0.0021445414 -7.014383e-04 4.990521e-03
## PC111 -0.0033480307 -6.212560e-03 -4.835014e-04
## PC113 0.0016276097 -1.241969e-03 4.497188e-03
## PC114 -0.0028422939 -5.706122e-03 2.153468e-05
## PC115 -0.0057720542 -8.656378e-03 -2.887730e-03
## PC118 0.0023483540 -5.493700e-04 5.246078e-03
## PC119 -0.0028879482 -5.781806e-03 5.910083e-06
## PC122 0.0025859779 -3.270246e-04 5.498980e-03
## PC123 -0.0024398312 -5.358963e-03 4.793004e-04
## PC124 0.0016884637 -1.237151e-03 4.614079e-03
## PC125 0.0020562283 -8.782947e-04 4.990751e-03
## PC127 0.0023169044 -5.861867e-04 5.219995e-03
## PC128 -0.0019080380 -4.835402e-03 1.019326e-03
## PC131 -0.0039830944 -6.925845e-03 -1.040343e-03
## PC133 -0.0014171974 -4.370144e-03 1.535750e-03
## PC134 0.0045785462 1.647384e-03 7.509709e-03
## PC135 0.0030155686 7.197429e-05 5.959163e-03
## PC138 0.0018387452 -1.142617e-03 4.820108e-03
## PC139 -0.0034859165 -6.452569e-03 -5.192640e-04
## PC143 0.0020890014 -9.103155e-04 5.088318e-03
## PC144 0.0025042869 -4.868277e-04 5.495401e-03
## PC145 0.0017490944 -1.253714e-03 4.751903e-03
## PC146 0.0046938976 1.679202e-03 7.708593e-03
## PC148 -0.0020388941 -5.021753e-03 9.439644e-04
## PC151 0.0030104170 -2.335209e-05 6.044186e-03
## PC153 0.0033871778 3.669846e-04 6.407371e-03
## PC154 -0.0036129566 -6.648374e-03 -5.775390e-04
## PC155 0.0032444401 2.058263e-04 6.283054e-03
## PC156 0.0033817945 3.344581e-04 6.429131e-03
## PC159 0.0057040318 2.664389e-03 8.743675e-03
## PC161 0.0015546860 -1.486372e-03 4.595744e-03
## PC162 -0.0051450187 -8.221766e-03 -2.068271e-03
## PC163 0.0025833525 -4.850980e-04 5.651803e-03Test
if (algo.forward.caret == TRUE){
test.model(model=model.forward, test=data.test
,method = 'leapForward',subopt = NULL
,formula = formula, feature.names = feature.names, label.names = label.names
,id = id
,draw.limits = TRUE, transformation = t)
}## [1] "Summary of predicted values: "
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 4.639 4.961 5.012 5.001 5.049 5.143
## [1] "leapForward Test MSE: 0.0138580579096168"
## [1] "leapForward Test RMSE: 0.117720252758889"
## [1] "leapForward Test MSE (Org Scale): 82.2350242465757"
## [1] "leapForward Test RMSE (Org Scale): 9.06835289601015"
Backward Elimination with CV
Train
if (algo.backward.caret == TRUE){
set.seed(1)
returned = train.caret.glmselect(formula = formula
,data = data.train
,method = "leapBackward"
,feature.names = feature.names)
model.backward = returned$model
id = returned$id
}## Aggregating results
## Selecting tuning parameters
## Fitting nvmax = 104 on full training set
## [1] "All models results"
## nvmax RMSE Rsquared MAE RMSESD RsquaredSD MAESD
## 1 1 0.1350468 0.08479660 0.10436184 0.005200049 0.01674113 0.002954202
## 2 2 0.1339628 0.09935862 0.10371363 0.005504447 0.01832821 0.003125743
## 3 3 0.1323635 0.12089088 0.10239954 0.005815779 0.02088009 0.003384538
## 4 4 0.1318132 0.12800310 0.10189097 0.005452716 0.01669327 0.003230049
## 5 5 0.1304285 0.14641271 0.10072021 0.005540135 0.01964057 0.003224118
## 6 6 0.1297260 0.15545312 0.10010572 0.005332458 0.01959561 0.002999176
## 7 7 0.1296458 0.15676998 0.10011934 0.005408872 0.01921091 0.003198788
## 8 8 0.1292860 0.16166820 0.09983246 0.005666917 0.02223766 0.003270292
## 9 9 0.1288372 0.16765598 0.09957128 0.005687598 0.02264859 0.003320170
## 10 10 0.1283193 0.17429662 0.09917594 0.005966020 0.02433558 0.003541938
## 11 11 0.1279362 0.17921957 0.09888127 0.005983356 0.02473557 0.003442295
## 12 12 0.1276569 0.18260370 0.09866195 0.005781548 0.02152010 0.003269757
## 13 13 0.1272739 0.18759117 0.09845644 0.005768872 0.02351046 0.003179434
## 14 14 0.1271615 0.18912503 0.09835234 0.005751381 0.02366383 0.003130328
## 15 15 0.1268642 0.19307028 0.09806442 0.005948943 0.02602667 0.003223252
## 16 16 0.1266694 0.19544374 0.09789322 0.005856941 0.02430375 0.003202948
## 17 17 0.1264706 0.19794585 0.09769118 0.005836174 0.02458856 0.003211562
## 18 18 0.1264844 0.19784441 0.09761652 0.005839495 0.02497885 0.003228483
## 19 19 0.1264275 0.19857322 0.09763926 0.005815373 0.02587255 0.003356488
## 20 20 0.1263052 0.20012438 0.09754751 0.005853704 0.02690377 0.003357624
## 21 21 0.1263884 0.19900583 0.09752871 0.005791377 0.02509730 0.003267652
## 22 22 0.1263051 0.20012161 0.09751512 0.005871821 0.02659607 0.003378924
## 23 23 0.1263833 0.19920885 0.09756776 0.005879425 0.02633925 0.003369958
## 24 24 0.1264223 0.19868676 0.09764942 0.005783628 0.02439144 0.003254422
## 25 25 0.1265097 0.19760003 0.09770993 0.005654214 0.02347045 0.003139757
## 26 26 0.1263927 0.19910993 0.09762567 0.005763593 0.02351943 0.003075068
## 27 27 0.1263814 0.19939537 0.09763183 0.005665547 0.02346896 0.003028282
## 28 28 0.1264759 0.19825074 0.09773256 0.005612793 0.02317772 0.002975545
## 29 29 0.1265454 0.19753824 0.09779892 0.005725031 0.02481153 0.003079489
## 30 30 0.1265390 0.19769106 0.09782618 0.005719897 0.02490035 0.003116986
## 31 31 0.1265541 0.19751539 0.09775613 0.005613531 0.02382063 0.003060166
## 32 32 0.1265618 0.19748093 0.09775847 0.005632815 0.02439437 0.003037837
## 33 33 0.1266044 0.19708571 0.09776977 0.005623306 0.02367647 0.002977068
## 34 34 0.1266824 0.19630060 0.09779546 0.005561872 0.02369771 0.002961893
## 35 35 0.1267466 0.19550167 0.09788808 0.005532787 0.02223223 0.002938956
## 36 36 0.1267913 0.19505671 0.09793542 0.005516065 0.02268444 0.002909473
## 37 37 0.1267420 0.19564293 0.09790417 0.005452299 0.02218800 0.002888763
## 38 38 0.1267693 0.19534713 0.09797083 0.005391634 0.02254449 0.002786412
## 39 39 0.1266941 0.19621807 0.09792208 0.005443768 0.02270683 0.002867403
## 40 40 0.1266032 0.19731311 0.09784475 0.005453620 0.02362891 0.002823375
## 41 41 0.1266487 0.19686721 0.09784641 0.005438635 0.02263536 0.002741763
## 42 42 0.1266494 0.19690176 0.09790198 0.005535586 0.02286920 0.002815589
## 43 43 0.1266414 0.19702178 0.09788982 0.005505565 0.02269165 0.002826998
## 44 44 0.1265910 0.19759202 0.09788469 0.005419004 0.02186087 0.002753382
## 45 45 0.1265590 0.19806497 0.09788721 0.005415209 0.02182409 0.002714861
## 46 46 0.1264753 0.19906952 0.09781345 0.005378691 0.02182379 0.002697631
## 47 47 0.1264665 0.19923416 0.09779211 0.005412107 0.02339531 0.002787665
## 48 48 0.1264306 0.19973851 0.09776269 0.005428465 0.02368400 0.002846922
## 49 49 0.1264553 0.19944771 0.09778577 0.005451932 0.02384344 0.002878485
## 50 50 0.1265133 0.19882190 0.09784700 0.005461735 0.02433038 0.002932090
## 51 51 0.1265147 0.19886789 0.09782985 0.005351818 0.02448614 0.002879602
## 52 52 0.1265157 0.19893644 0.09779332 0.005421718 0.02555480 0.002861577
## 53 53 0.1264570 0.19971512 0.09774071 0.005418478 0.02632611 0.002892773
## 54 54 0.1264024 0.20043931 0.09772371 0.005448019 0.02603882 0.002920868
## 55 55 0.1265126 0.19924728 0.09779898 0.005559385 0.02607842 0.003011734
## 56 56 0.1265417 0.19895376 0.09778923 0.005641219 0.02625676 0.003057185
## 57 57 0.1264784 0.19967584 0.09775607 0.005622519 0.02575725 0.003060311
## 58 58 0.1264265 0.20027907 0.09769431 0.005627343 0.02580792 0.003111743
## 59 59 0.1263829 0.20080840 0.09763272 0.005562019 0.02530009 0.003113028
## 60 60 0.1263945 0.20070174 0.09763835 0.005529801 0.02507800 0.003095519
## 61 61 0.1264140 0.20046460 0.09764594 0.005481315 0.02505148 0.003073537
## 62 62 0.1264087 0.20052054 0.09765076 0.005458976 0.02479817 0.003043535
## 63 63 0.1263678 0.20100727 0.09758721 0.005456709 0.02479016 0.003053931
## 64 64 0.1264259 0.20031310 0.09763725 0.005424525 0.02429027 0.003013452
## 65 65 0.1263915 0.20074182 0.09762058 0.005474633 0.02472960 0.003067736
## 66 66 0.1263666 0.20102402 0.09763115 0.005459813 0.02481906 0.003069059
## 67 67 0.1263352 0.20143800 0.09762473 0.005419271 0.02429941 0.003044765
## 68 68 0.1263599 0.20113250 0.09767271 0.005387661 0.02385602 0.003002265
## 69 69 0.1263252 0.20151057 0.09766418 0.005393598 0.02349664 0.003041828
## 70 70 0.1263002 0.20181473 0.09765565 0.005374837 0.02309418 0.003011970
## 71 71 0.1263319 0.20152204 0.09765607 0.005424528 0.02345475 0.003059108
## 72 72 0.1263507 0.20134278 0.09765753 0.005409843 0.02326292 0.003029063
## 73 73 0.1263127 0.20174794 0.09764753 0.005408784 0.02371303 0.003030095
## 74 74 0.1262823 0.20213249 0.09763507 0.005380452 0.02341940 0.003051790
## 75 75 0.1262725 0.20223029 0.09763208 0.005304047 0.02236670 0.003016053
## 76 76 0.1262371 0.20264131 0.09758679 0.005292581 0.02168862 0.002952700
## 77 77 0.1262565 0.20241892 0.09762932 0.005299260 0.02191771 0.002986881
## 78 78 0.1262637 0.20234448 0.09764313 0.005310396 0.02162498 0.002980389
## 79 79 0.1262544 0.20250739 0.09764341 0.005361154 0.02205173 0.003021316
## 80 80 0.1262282 0.20283190 0.09760474 0.005351637 0.02188648 0.003037540
## 81 81 0.1261947 0.20320912 0.09756195 0.005370144 0.02142310 0.003045244
## 82 82 0.1262093 0.20305084 0.09757602 0.005407741 0.02185420 0.003112448
## 83 83 0.1261835 0.20338392 0.09755670 0.005398219 0.02174522 0.003121264
## 84 84 0.1261943 0.20328274 0.09754422 0.005395969 0.02155500 0.003151575
## 85 85 0.1261801 0.20351312 0.09750636 0.005366685 0.02186587 0.003144886
## 86 86 0.1262133 0.20312423 0.09750534 0.005379930 0.02243058 0.003187798
## 87 87 0.1262237 0.20307418 0.09750392 0.005375135 0.02298658 0.003205483
## 88 88 0.1262038 0.20325928 0.09749188 0.005369043 0.02236716 0.003147748
## 89 89 0.1261844 0.20346605 0.09745517 0.005386843 0.02254646 0.003137870
## 90 90 0.1261934 0.20336665 0.09747709 0.005363438 0.02261102 0.003123915
## 91 91 0.1262115 0.20318239 0.09747607 0.005327149 0.02229746 0.003105752
## 92 92 0.1262047 0.20326525 0.09745141 0.005331226 0.02242038 0.003132270
## 93 93 0.1261225 0.20423298 0.09736894 0.005299431 0.02271374 0.003095875
## 94 94 0.1261084 0.20441607 0.09739394 0.005335749 0.02319458 0.003102660
## 95 95 0.1261075 0.20443558 0.09738597 0.005357368 0.02297656 0.003099529
## 96 96 0.1260763 0.20481307 0.09738863 0.005369982 0.02279456 0.003082313
## 97 97 0.1260529 0.20509771 0.09737907 0.005358122 0.02234591 0.003048558
## 98 98 0.1260253 0.20541944 0.09735268 0.005372822 0.02191204 0.003049515
## 99 99 0.1259889 0.20583918 0.09732135 0.005405219 0.02221314 0.003082910
## 100 100 0.1259431 0.20637870 0.09728196 0.005414094 0.02208661 0.003088996
## 101 101 0.1259506 0.20631410 0.09728754 0.005405848 0.02170002 0.003091968
## 102 102 0.1259470 0.20637569 0.09728811 0.005414784 0.02210487 0.003112447
## 103 103 0.1259149 0.20675939 0.09727566 0.005431964 0.02230887 0.003145610
## 104 104 0.1259051 0.20690915 0.09728373 0.005450166 0.02258272 0.003171473
## 105 105 0.1259052 0.20691319 0.09728686 0.005450328 0.02273456 0.003193748
## 106 106 0.1259107 0.20687083 0.09728522 0.005454628 0.02284862 0.003198774
## 107 107 0.1259421 0.20653396 0.09731947 0.005455741 0.02303401 0.003209778
## 108 108 0.1259642 0.20628464 0.09733366 0.005451393 0.02285053 0.003210432
## 109 109 0.1259634 0.20631324 0.09732236 0.005428053 0.02250955 0.003172108
## 110 110 0.1259679 0.20631675 0.09732433 0.005452312 0.02253926 0.003188762
## 111 111 0.1259710 0.20628299 0.09731483 0.005405769 0.02232346 0.003160585
## 112 112 0.1259855 0.20608547 0.09732461 0.005368711 0.02188531 0.003127433
## 113 113 0.1259943 0.20601284 0.09729940 0.005382886 0.02194380 0.003143501
## 114 114 0.1259949 0.20597609 0.09728958 0.005376087 0.02186849 0.003160552
## 115 115 0.1259927 0.20600764 0.09729254 0.005369456 0.02205479 0.003167334
## 116 116 0.1260079 0.20583256 0.09731536 0.005373486 0.02195621 0.003168683
## 117 117 0.1260436 0.20544271 0.09734919 0.005381737 0.02214890 0.003172554
## 118 118 0.1260861 0.20496671 0.09737930 0.005377389 0.02204373 0.003175491
## 119 119 0.1260895 0.20493554 0.09738733 0.005390235 0.02226188 0.003183898
## 120 120 0.1260932 0.20491415 0.09739337 0.005377898 0.02206991 0.003183617
## 121 121 0.1261028 0.20481386 0.09741028 0.005383794 0.02211571 0.003185459
## 122 122 0.1261127 0.20471560 0.09741576 0.005400097 0.02231831 0.003204656
## 123 123 0.1261227 0.20461441 0.09742624 0.005400570 0.02239069 0.003201025
## 124 124 0.1261518 0.20429543 0.09745291 0.005401608 0.02242096 0.003192159
## 125 125 0.1261578 0.20424997 0.09746621 0.005426437 0.02270965 0.003225716
## 126 126 0.1261498 0.20435044 0.09746041 0.005430491 0.02253847 0.003242284
## 127 127 0.1261719 0.20411142 0.09747511 0.005455823 0.02276624 0.003253842
## 128 128 0.1261756 0.20408420 0.09747046 0.005439971 0.02253104 0.003241995
## 129 129 0.1261882 0.20394601 0.09748106 0.005432678 0.02246081 0.003239384
## 130 130 0.1261895 0.20393660 0.09748744 0.005443065 0.02266185 0.003250012
## 131 131 0.1261799 0.20405202 0.09748314 0.005456300 0.02277028 0.003249011
## 132 132 0.1261836 0.20401152 0.09748293 0.005452311 0.02268762 0.003255315
## 133 133 0.1261815 0.20401891 0.09747862 0.005445579 0.02247635 0.003247413
## 134 134 0.1261903 0.20392632 0.09748109 0.005431535 0.02239767 0.003242716
## 135 135 0.1262091 0.20372009 0.09749865 0.005434270 0.02239300 0.003260230
## 136 136 0.1261984 0.20383965 0.09748288 0.005457746 0.02252193 0.003274988
## 137 137 0.1261996 0.20384482 0.09748329 0.005463124 0.02247554 0.003277424
## 138 138 0.1261933 0.20390311 0.09748450 0.005451886 0.02239290 0.003265183
## 139 139 0.1261869 0.20397962 0.09748228 0.005445921 0.02238047 0.003261087
## 140 140 0.1262163 0.20365760 0.09750413 0.005445294 0.02225625 0.003261575
## 141 141 0.1262184 0.20362681 0.09749855 0.005442033 0.02214024 0.003253918
## 142 142 0.1262113 0.20370244 0.09750014 0.005437250 0.02213571 0.003249088
## 143 143 0.1262096 0.20372876 0.09750517 0.005438812 0.02213515 0.003254118
## 144 144 0.1262141 0.20367935 0.09750982 0.005435561 0.02206687 0.003248656
## 145 145 0.1262060 0.20376658 0.09750987 0.005442310 0.02209094 0.003254436
## 146 146 0.1262051 0.20377735 0.09750987 0.005451347 0.02213734 0.003253233
## 147 147 0.1262041 0.20378497 0.09751183 0.005461005 0.02219693 0.003258773
## 148 148 0.1261995 0.20384308 0.09751107 0.005465376 0.02218786 0.003265796
## 149 149 0.1262044 0.20378893 0.09751134 0.005468523 0.02218228 0.003262595
## 150 150 0.1262027 0.20381211 0.09750763 0.005468089 0.02217296 0.003261503
## 151 151 0.1262090 0.20373619 0.09751575 0.005460952 0.02209842 0.003255790
## 152 152 0.1262037 0.20378890 0.09751525 0.005462154 0.02208358 0.003251597
## 153 153 0.1262071 0.20375273 0.09752227 0.005465137 0.02207422 0.003253257
## 154 154 0.1262073 0.20375241 0.09752350 0.005463187 0.02208191 0.003250070
## 155 155 0.1262034 0.20380067 0.09752149 0.005463287 0.02209506 0.003248892
## 156 156 0.1262023 0.20381833 0.09751753 0.005464455 0.02209686 0.003251020
## 157 157 0.1262058 0.20377730 0.09752006 0.005464224 0.02208234 0.003250305
## 158 158 0.1262066 0.20376829 0.09752177 0.005461336 0.02206925 0.003248812
## 159 159 0.1262076 0.20375611 0.09752366 0.005460250 0.02206564 0.003248059
## 160 160 0.1262103 0.20372445 0.09752663 0.005458698 0.02202558 0.003245804
## 161 161 0.1262111 0.20371422 0.09752690 0.005459543 0.02202359 0.003246306
## 162 162 0.1262102 0.20372134 0.09752614 0.005458645 0.02202366 0.003245864
## 163 163 0.1262109 0.20371360 0.09752644 0.005459111 0.02202303 0.003246147
## 164 164 0.1262107 0.20371699 0.09752633 0.005459230 0.02202556 0.003246293
## [1] "Best Model"
## nvmax
## 104 104
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## [1] "Coefficients of final model:"
## Estimate 2.5 % 97.5 %
## (Intercept) 5.0014222113 4.998174e+00 5.004670e+00
## PC1 -0.0016577612 -1.939353e-03 -1.376169e-03
## PC2 -0.0035749327 -3.860566e-03 -3.289299e-03
## PC3 -0.0015492645 -1.835588e-03 -1.262941e-03
## PC4 -0.0012192821 -1.510584e-03 -9.279801e-04
## PC5 0.0007734032 4.716727e-04 1.075134e-03
## PC6 -0.0004590054 -7.604569e-04 -1.575540e-04
## PC7 -0.0007433374 -1.051814e-03 -4.348603e-04
## PC8 -0.0002119523 -5.244417e-04 1.005370e-04
## PC9 -0.0001764765 -4.988891e-04 1.459362e-04
## PC11 -0.0021129296 -2.464339e-03 -1.761520e-03
## PC12 -0.0017534984 -2.125579e-03 -1.381418e-03
## PC13 0.0011482032 7.702755e-04 1.526131e-03
## PC14 0.0009457513 5.550094e-04 1.336493e-03
## PC16 0.0013424822 9.427021e-04 1.742262e-03
## PC17 -0.0008021447 -1.226711e-03 -3.775788e-04
## PC18 -0.0014706365 -1.913788e-03 -1.027485e-03
## PC20 0.0017180699 1.230600e-03 2.205540e-03
## PC21 0.0002442162 -2.628232e-04 7.512556e-04
## PC22 0.0005330761 -2.604048e-04 1.326557e-03
## PC23 0.0012883717 3.112099e-04 2.265533e-03
## PC24 -0.0032749970 -4.424187e-03 -2.125807e-03
## PC25 0.0011059619 -1.760535e-04 2.387977e-03
## PC26 0.0014136753 9.433858e-05 2.733012e-03
## PC27 0.0015993679 2.721977e-04 2.926538e-03
## PC28 0.0005992156 -7.492971e-04 1.947728e-03
## PC29 0.0015253507 4.989974e-05 3.000802e-03
## PC31 -0.0009890918 -2.608820e-03 6.306362e-04
## PC32 -0.0027516041 -4.387448e-03 -1.115760e-03
## PC33 0.0012886128 -3.839173e-04 2.961143e-03
## PC34 0.0040405432 2.272817e-03 5.808269e-03
## PC37 -0.0013894136 -3.368896e-03 5.900690e-04
## PC38 0.0011026820 -9.574556e-04 3.162820e-03
## PC44 0.0017203442 -4.656027e-04 3.906291e-03
## PC45 -0.0013110319 -3.499879e-03 8.778154e-04
## PC47 -0.0015943566 -3.831725e-03 6.430123e-04
## PC48 0.0012636314 -1.018414e-03 3.545677e-03
## PC49 0.0011182781 -1.169225e-03 3.405782e-03
## PC57 -0.0016675666 -4.072766e-03 7.376329e-04
## PC59 0.0024626269 8.613876e-05 4.839115e-03
## PC60 -0.0013218780 -3.747980e-03 1.104224e-03
## PC63 -0.0021916039 -4.637387e-03 2.541793e-04
## PC64 -0.0019642192 -4.420613e-03 4.921741e-04
## PC65 -0.0011496140 -3.600145e-03 1.300917e-03
## PC66 -0.0023281552 -4.811451e-03 1.551403e-04
## PC68 0.0026001944 9.787031e-05 5.102518e-03
## PC69 0.0015913446 -9.243813e-04 4.107070e-03
## PC71 0.0028929184 3.769245e-04 5.408912e-03
## PC74 -0.0016118474 -4.179097e-03 9.554023e-04
## PC75 -0.0034053759 -5.986997e-03 -8.237550e-04
## PC77 0.0017379226 -8.472808e-04 4.323126e-03
## PC78 0.0014921819 -1.102725e-03 4.087089e-03
## PC79 0.0024692020 -1.508188e-04 5.089223e-03
## PC80 -0.0012210840 -3.885507e-03 1.443339e-03
## PC81 0.0038126686 1.157388e-03 6.467949e-03
## PC83 -0.0025480822 -5.199592e-03 1.034278e-04
## PC84 0.0034582002 7.917886e-04 6.124612e-03
## PC85 0.0046426930 1.936655e-03 7.348731e-03
## PC86 -0.0021190342 -4.818604e-03 5.805357e-04
## PC87 0.0079850241 5.253348e-03 1.071670e-02
## PC88 -0.0019026781 -4.673888e-03 8.685318e-04
## PC89 -0.0025753556 -5.300173e-03 1.494620e-04
## PC90 -0.0019867324 -4.723925e-03 7.504599e-04
## PC94 -0.0037767007 -6.541284e-03 -1.012117e-03
## PC96 -0.0038427244 -6.646385e-03 -1.039064e-03
## PC97 -0.0018198439 -4.607061e-03 9.673736e-04
## PC99 -0.0021647930 -4.966449e-03 6.368633e-04
## PC102 -0.0024111155 -5.250977e-03 4.287461e-04
## PC103 0.0028049658 -1.258909e-05 5.622521e-03
## PC104 -0.0037227926 -6.551281e-03 -8.943046e-04
## PC105 0.0030198383 1.816261e-04 5.858050e-03
## PC106 0.0036544913 8.294313e-04 6.479551e-03
## PC109 0.0021413254 -7.045688e-04 4.987220e-03
## PC111 -0.0033544759 -6.218890e-03 -4.900620e-04
## PC113 0.0016187830 -1.250646e-03 4.488212e-03
## PC114 -0.0028390509 -5.702793e-03 2.469165e-05
## PC115 -0.0057876949 -8.671712e-03 -2.903677e-03
## PC118 0.0023517131 -5.459234e-04 5.249350e-03
## PC119 -0.0028830942 -5.776853e-03 1.066510e-05
## PC122 0.0025881068 -3.248141e-04 5.501028e-03
## PC123 -0.0024474000 -5.366401e-03 4.716008e-04
## PC124 0.0016762785 -1.249121e-03 4.601678e-03
## PC125 0.0020406172 -8.936028e-04 4.974837e-03
## PC127 0.0023154697 -5.875423e-04 5.218482e-03
## PC128 -0.0019045648 -4.831840e-03 1.022711e-03
## PC131 -0.0039823516 -6.925024e-03 -1.039679e-03
## PC133 -0.0014211645 -4.374019e-03 1.531690e-03
## PC134 0.0045632507 1.632382e-03 7.494119e-03
## PC135 0.0030116658 6.816370e-05 5.955168e-03
## PC138 0.0018376645 -1.143618e-03 4.818947e-03
## PC139 -0.0034823391 -6.448901e-03 -5.157771e-04
## PC143 0.0020985169 -9.006384e-04 5.097672e-03
## PC144 0.0025130617 -4.779036e-04 5.504027e-03
## PC145 0.0017584098 -1.244241e-03 4.761060e-03
## PC146 0.0046934971 1.678882e-03 7.708112e-03
## PC148 -0.0020385676 -5.021347e-03 9.442115e-04
## PC151 0.0030021294 -3.149765e-05 6.035757e-03
## PC153 0.0033895689 3.694610e-04 6.409677e-03
## PC154 -0.0036163082 -6.651635e-03 -5.809812e-04
## PC155 0.0032510431 2.125490e-04 6.289537e-03
## PC156 0.0033882955 3.410777e-04 6.435513e-03
## PC159 0.0057078538 2.668305e-03 8.747403e-03
## PC161 0.0015612292 -1.479710e-03 4.602168e-03
## PC162 -0.0051649052 -8.241223e-03 -2.088588e-03
## PC163 0.0025996682 -4.684657e-04 5.667802e-03Test
if (algo.backward.caret == TRUE){
test.model(model.backward, data.test
,method = 'leapBackward',subopt = NULL
,formula = formula, feature.names = feature.names, label.names = label.names
,id = id
,draw.limits = TRUE, transformation = t)
}## [1] "Summary of predicted values: "
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 4.643 4.961 5.012 5.001 5.049 5.143
## [1] "leapBackward Test MSE: 0.0138487130654014"
## [1] "leapBackward Test RMSE: 0.117680555171198"
## [1] "leapBackward Test MSE (Org Scale): 82.1848665615533"
## [1] "leapBackward Test RMSE (Org Scale): 9.06558693971622"
Stepwise Selection with CV
Train
if (algo.stepwise.caret == TRUE){
set.seed(1)
returned = train.caret.glmselect(formula = formula
,data = data.train
,method = "leapSeq"
,feature.names = feature.names)
model.stepwise = returned$model
id = returned$id
}## Aggregating results
## Selecting tuning parameters
## Fitting nvmax = 105 on full training set
## [1] "All models results"
## nvmax RMSE Rsquared MAE RMSESD RsquaredSD MAESD
## 1 1 0.1350468 0.08479660 0.10436184 0.005200049 0.01674113 0.002954202
## 2 2 0.1339628 0.09935862 0.10371363 0.005504447 0.01832821 0.003125743
## 3 3 0.1325279 0.11859544 0.10261175 0.005695304 0.02051365 0.003329322
## 4 4 0.1322772 0.12208289 0.10206422 0.005339563 0.02078229 0.003118272
## 5 5 0.1305639 0.14426308 0.10100557 0.005042205 0.01403455 0.002731516
## 6 6 0.1316835 0.12976030 0.10173813 0.005316761 0.02257861 0.003023353
## 7 7 0.1296458 0.15676998 0.10011934 0.005408872 0.01921091 0.003198788
## 8 8 0.1292860 0.16166820 0.09983246 0.005666917 0.02223766 0.003270292
## 9 9 0.1288372 0.16765598 0.09957128 0.005687598 0.02264859 0.003320170
## 10 10 0.1283193 0.17429662 0.09917594 0.005966020 0.02433558 0.003541938
## 11 11 0.1279362 0.17921957 0.09888127 0.005983356 0.02473557 0.003442295
## 12 12 0.1281969 0.17548221 0.09905509 0.005351854 0.01623643 0.002913054
## 13 13 0.1274936 0.18459777 0.09861919 0.005801784 0.02498022 0.003233391
## 14 14 0.1271615 0.18912503 0.09835234 0.005751381 0.02366383 0.003130328
## 15 15 0.1275661 0.18360676 0.09858862 0.005819577 0.02996811 0.003329440
## 16 16 0.1266694 0.19544374 0.09789322 0.005856941 0.02430375 0.003202948
## 17 17 0.1264706 0.19794585 0.09769118 0.005836174 0.02458856 0.003211562
## 18 18 0.1264844 0.19784441 0.09761652 0.005839495 0.02497885 0.003228483
## 19 19 0.1264275 0.19857322 0.09763926 0.005815373 0.02587255 0.003356488
## 20 20 0.1263052 0.20012438 0.09754751 0.005853704 0.02690377 0.003357624
## 21 21 0.1263884 0.19900583 0.09752871 0.005791377 0.02509730 0.003267652
## 22 22 0.1263051 0.20012161 0.09751512 0.005871821 0.02659607 0.003378924
## 23 23 0.1267050 0.19499902 0.09786119 0.005624592 0.02720583 0.003299839
## 24 24 0.1264146 0.19869760 0.09778952 0.005779477 0.02438728 0.003300492
## 25 25 0.1265097 0.19760003 0.09770993 0.005654214 0.02347045 0.003139757
## 26 26 0.1263927 0.19910993 0.09762567 0.005763593 0.02351943 0.003075068
## 27 27 0.1263814 0.19939537 0.09763183 0.005665547 0.02346896 0.003028282
## 28 28 0.1267634 0.19454072 0.09798707 0.005689976 0.02146966 0.002919610
## 29 29 0.1265454 0.19753824 0.09779892 0.005725031 0.02481153 0.003079489
## 30 30 0.1265390 0.19769106 0.09782618 0.005719897 0.02490035 0.003116986
## 31 31 0.1265541 0.19751539 0.09775613 0.005613531 0.02382063 0.003060166
## 32 32 0.1265618 0.19748093 0.09775847 0.005632815 0.02439437 0.003037837
## 33 33 0.1266044 0.19708571 0.09776977 0.005623306 0.02367647 0.002977068
## 34 34 0.1266189 0.19706632 0.09778340 0.005575182 0.02371033 0.002961167
## 35 35 0.1267466 0.19550167 0.09788808 0.005532787 0.02223223 0.002938956
## 36 36 0.1267695 0.19528058 0.09793055 0.005501084 0.02251962 0.002907074
## 37 37 0.1267420 0.19564293 0.09790417 0.005452299 0.02218800 0.002888763
## 38 38 0.1266638 0.19647283 0.09790816 0.005330265 0.02205737 0.002762618
## 39 39 0.1266917 0.19610127 0.09784108 0.005447161 0.02289125 0.002866402
## 40 40 0.1266227 0.19715789 0.09789099 0.005471754 0.02366100 0.002851723
## 41 41 0.1266699 0.19660533 0.09790882 0.005442517 0.02268889 0.002774760
## 42 42 0.1266494 0.19690176 0.09790198 0.005535586 0.02286920 0.002815589
## 43 43 0.1266819 0.19639631 0.09786647 0.005533537 0.02298357 0.002805611
## 44 44 0.1266156 0.19713052 0.09784906 0.005436428 0.02209167 0.002719508
## 45 45 0.1264311 0.19935758 0.09788548 0.005371560 0.02153190 0.002703640
## 46 46 0.1265030 0.19873032 0.09783505 0.005437657 0.02215237 0.002742781
## 47 47 0.1264665 0.19923416 0.09779211 0.005412107 0.02339531 0.002787665
## 48 48 0.1265336 0.19846547 0.09786012 0.005628169 0.02502365 0.003028937
## 49 49 0.1264494 0.19952905 0.09777268 0.005453521 0.02401244 0.002891190
## 50 50 0.1264070 0.19990081 0.09789331 0.005463733 0.02389122 0.002946627
## 51 51 0.1265382 0.19858572 0.09784181 0.005406872 0.02427270 0.002905345
## 52 52 0.1265645 0.19840160 0.09790344 0.005510323 0.02585609 0.002960722
## 53 53 0.1267176 0.19649334 0.09801672 0.005422541 0.02077710 0.002775333
## 54 54 0.1263742 0.20066805 0.09771197 0.005452019 0.02599711 0.002918154
## 55 55 0.1266051 0.19763710 0.09790074 0.005789355 0.02821974 0.003196533
## 56 56 0.1265556 0.19841681 0.09775886 0.005709270 0.02677930 0.003060421
## 57 57 0.1265227 0.19898943 0.09782542 0.005672396 0.02662914 0.003099303
## 58 58 0.1264144 0.19997077 0.09775297 0.005629872 0.02573608 0.003170875
## 59 59 0.1264182 0.20001696 0.09775194 0.005797404 0.02671245 0.003289860
## 60 60 0.1264646 0.19988603 0.09761342 0.005503591 0.02442307 0.003108297
## 61 61 0.1265138 0.19900750 0.09765880 0.005556988 0.02601605 0.003089252
## 62 62 0.1264087 0.20052054 0.09765076 0.005458976 0.02479817 0.003043535
## 63 63 0.1263366 0.20129863 0.09754349 0.005451967 0.02435507 0.003076678
## 64 64 0.1264259 0.20031310 0.09763725 0.005424525 0.02429027 0.003013452
## 65 65 0.1263915 0.20074182 0.09762058 0.005474633 0.02472960 0.003067736
## 66 66 0.1265739 0.19831297 0.09787518 0.005459195 0.01984935 0.002945129
## 67 67 0.1263352 0.20143800 0.09762473 0.005419271 0.02429941 0.003044765
## 68 68 0.1263604 0.20111577 0.09767420 0.005388026 0.02386378 0.003004040
## 69 69 0.1263256 0.20149491 0.09766525 0.005393875 0.02350204 0.003042984
## 70 70 0.1263002 0.20181473 0.09765565 0.005374837 0.02309418 0.003011970
## 71 71 0.1264214 0.20012020 0.09769444 0.005496297 0.02441083 0.003104155
## 72 72 0.1263507 0.20134278 0.09765753 0.005409843 0.02326292 0.003029063
## 73 73 0.1263248 0.20132052 0.09774986 0.005412939 0.02402634 0.003091156
## 74 74 0.1262823 0.20213249 0.09763507 0.005380452 0.02341940 0.003051790
## 75 75 0.1263350 0.20120931 0.09777582 0.005307162 0.02260807 0.003082305
## 76 76 0.1263365 0.20127569 0.09769852 0.005358018 0.02270595 0.002991455
## 77 77 0.1262740 0.20231825 0.09755218 0.005297567 0.02210017 0.003043057
## 78 78 0.1262020 0.20299214 0.09749060 0.005452566 0.02256629 0.003352238
## 79 79 0.1263419 0.20138368 0.09768639 0.005361393 0.02297008 0.003068239
## 80 80 0.1262581 0.20242680 0.09759276 0.005346043 0.02206966 0.003104953
## 81 81 0.1261947 0.20320912 0.09756195 0.005370144 0.02142310 0.003045244
## 82 82 0.1262659 0.20207048 0.09762445 0.005378114 0.02354856 0.003131447
## 83 83 0.1261996 0.20313799 0.09741336 0.005420777 0.02150601 0.003382701
## 84 84 0.1263164 0.20174346 0.09762979 0.005661491 0.02340628 0.003298319
## 85 85 0.1261801 0.20351312 0.09750636 0.005366685 0.02186587 0.003144886
## 86 86 0.1261970 0.20298678 0.09749973 0.005511911 0.02358881 0.003436087
## 87 87 0.1262338 0.20292624 0.09745802 0.005705640 0.02566215 0.003468153
## 88 88 0.1262483 0.20249283 0.09757617 0.005370057 0.02277543 0.003130502
## 89 89 0.1261955 0.20335164 0.09746301 0.005393621 0.02259959 0.003139729
## 90 90 0.1261934 0.20336665 0.09747709 0.005363438 0.02261102 0.003123915
## 91 91 0.1264311 0.20059007 0.09762620 0.005652167 0.02467497 0.003284455
## 92 92 0.1263402 0.20160197 0.09756722 0.005326981 0.01920001 0.003055152
## 93 93 0.1261621 0.20377905 0.09742235 0.005346787 0.02257374 0.003090141
## 94 94 0.1261084 0.20441607 0.09739394 0.005335749 0.02319458 0.003102660
## 95 95 0.1264174 0.20066596 0.09761633 0.005612220 0.02117898 0.003247363
## 96 96 0.1263164 0.20160242 0.09747864 0.005393009 0.01988180 0.003042558
## 97 97 0.1260800 0.20479082 0.09739708 0.005360230 0.02250364 0.003048303
## 98 98 0.1260321 0.20510429 0.09734445 0.005369648 0.02292541 0.003062055
## 99 99 0.1260488 0.20496114 0.09736048 0.005422419 0.02276596 0.003102894
## 100 100 0.1259479 0.20612362 0.09728252 0.005417393 0.02255106 0.003113881
## 101 101 0.1260789 0.20478302 0.09743580 0.005672517 0.02360294 0.003332230
## 102 102 0.1259519 0.20631170 0.09729305 0.005411918 0.02220200 0.003113944
## 103 103 0.1259241 0.20663886 0.09728295 0.005434298 0.02236920 0.003148814
## 104 104 0.1259247 0.20625351 0.09737047 0.005440436 0.02334962 0.003172490
## 105 105 0.1259052 0.20691319 0.09728686 0.005450328 0.02273456 0.003193748
## 106 106 0.1259107 0.20687083 0.09728522 0.005454628 0.02284862 0.003198774
## 107 107 0.1260101 0.20568038 0.09744929 0.005601612 0.02401082 0.003431009
## 108 108 0.1259642 0.20628464 0.09733366 0.005451393 0.02285053 0.003210432
## 109 109 0.1259234 0.20664633 0.09727907 0.005519219 0.02299484 0.003275447
## 110 110 0.1259679 0.20631675 0.09732433 0.005452312 0.02253926 0.003188762
## 111 111 0.1260582 0.20535046 0.09740466 0.005464953 0.02291757 0.003200165
## 112 112 0.1259680 0.20629315 0.09730748 0.005372698 0.02230929 0.003141726
## 113 113 0.1259640 0.20616394 0.09732440 0.005390251 0.02248070 0.003143256
## 114 114 0.1260355 0.20535300 0.09733967 0.005354253 0.02291612 0.003179052
## 115 115 0.1261254 0.20409338 0.09731557 0.005366230 0.01961667 0.003083218
## 116 116 0.1260079 0.20583256 0.09731536 0.005373486 0.02195621 0.003168683
## 117 117 0.1260436 0.20544271 0.09734919 0.005381737 0.02214890 0.003172554
## 118 118 0.1260755 0.20509228 0.09737181 0.005379707 0.02229585 0.003181631
## 119 119 0.1260895 0.20493554 0.09738733 0.005390235 0.02226188 0.003183898
## 120 120 0.1263104 0.20220053 0.09758767 0.005364904 0.01936782 0.003103567
## 121 121 0.1260962 0.20472831 0.09736875 0.005415717 0.02214818 0.003287637
## 122 122 0.1261143 0.20470180 0.09741450 0.005400070 0.02232558 0.003205105
## 123 123 0.1261227 0.20461441 0.09742624 0.005400570 0.02239069 0.003201025
## 124 124 0.1261518 0.20429543 0.09745291 0.005401608 0.02242096 0.003192159
## 125 125 0.1261578 0.20424997 0.09746621 0.005426437 0.02270965 0.003225716
## 126 126 0.1262953 0.20257515 0.09754172 0.005414468 0.01938043 0.003185837
## 127 127 0.1261696 0.20413922 0.09746916 0.005456752 0.02279187 0.003256842
## 128 128 0.1261852 0.20396915 0.09749103 0.005445025 0.02258067 0.003243312
## 129 129 0.1262147 0.20356858 0.09753423 0.005488625 0.02285205 0.003325360
## 130 130 0.1263447 0.20176081 0.09759023 0.005456417 0.02307641 0.003211006
## 131 131 0.1263736 0.20171757 0.09760836 0.005442613 0.01887451 0.003171437
## 132 132 0.1261836 0.20401152 0.09748293 0.005452311 0.02268762 0.003255315
## 133 133 0.1261815 0.20401891 0.09747862 0.005445579 0.02247635 0.003247413
## 134 134 0.1261679 0.20413308 0.09754349 0.005494370 0.02291241 0.003280477
## 135 135 0.1262091 0.20372009 0.09749865 0.005434270 0.02239300 0.003260230
## 136 136 0.1262480 0.20322034 0.09750876 0.005439350 0.02202279 0.003263059
## 137 137 0.1261996 0.20384482 0.09748329 0.005463124 0.02247554 0.003277424
## 138 138 0.1260828 0.20500834 0.09743437 0.005464973 0.02236168 0.003256900
## 139 139 0.1261849 0.20371541 0.09752111 0.005545615 0.02305477 0.003364675
## 140 140 0.1262163 0.20365760 0.09750413 0.005445294 0.02225625 0.003261575
## 141 141 0.1262184 0.20362681 0.09749855 0.005442033 0.02214024 0.003253918
## 142 142 0.1262113 0.20370244 0.09750014 0.005437250 0.02213571 0.003249088
## 143 143 0.1263053 0.20262855 0.09763133 0.005445772 0.02297824 0.003233102
## 144 144 0.1262141 0.20367935 0.09750982 0.005435561 0.02206687 0.003248656
## 145 145 0.1262001 0.20374020 0.09749636 0.005455758 0.02205134 0.003286755
## 146 146 0.1261814 0.20394764 0.09749285 0.005444576 0.02203457 0.003244521
## 147 147 0.1262041 0.20378497 0.09751183 0.005461005 0.02219693 0.003258773
## 148 148 0.1261995 0.20384308 0.09751107 0.005465376 0.02218786 0.003265796
## 149 149 0.1262357 0.20335516 0.09755440 0.005450382 0.02284001 0.003274319
## 150 150 0.1262360 0.20343283 0.09755822 0.005537977 0.02257121 0.003341582
## 151 151 0.1261815 0.20399123 0.09746637 0.005466393 0.02208943 0.003255334
## 152 152 0.1262037 0.20378890 0.09751525 0.005462154 0.02208358 0.003251597
## 153 153 0.1262071 0.20375273 0.09752227 0.005465137 0.02207422 0.003253257
## 154 154 0.1263044 0.20258269 0.09759268 0.005451627 0.01997249 0.003208215
## 155 155 0.1262226 0.20347248 0.09756220 0.005477332 0.02224766 0.003305405
## 156 156 0.1262266 0.20347780 0.09755820 0.005409539 0.02160416 0.003155794
## 157 157 0.1262352 0.20332987 0.09754736 0.005486054 0.02230274 0.003287724
## 158 158 0.1262066 0.20376829 0.09752177 0.005461336 0.02206925 0.003248812
## 159 159 0.1262521 0.20331827 0.09758682 0.005460783 0.02232412 0.003230028
## 160 160 0.1262673 0.20308715 0.09761758 0.005446711 0.02135365 0.003222636
## 161 161 0.1261725 0.20408172 0.09750785 0.005462554 0.02197681 0.003258521
## 162 162 0.1262127 0.20363342 0.09752853 0.005431786 0.02181612 0.003215356
## 163 163 0.1262045 0.20378760 0.09751702 0.005461890 0.02212859 0.003251503
## 164 164 0.1262107 0.20371699 0.09752633 0.005459230 0.02202556 0.003246293
## [1] "Best Model"
## nvmax
## 105 105
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## [1] "Coefficients of final model:"
## Estimate 2.5 % 97.5 %
## (Intercept) 5.0014260845 4.998178e+00 5.004674e+00
## PC1 -0.0016578295 -1.939429e-03 -1.376230e-03
## PC2 -0.0035750955 -3.860737e-03 -3.289454e-03
## PC3 -0.0015501926 -1.836532e-03 -1.263853e-03
## PC4 -0.0012180774 -1.509401e-03 -9.267541e-04
## PC5 0.0007735608 4.718221e-04 1.075300e-03
## PC6 -0.0004595017 -7.609634e-04 -1.580401e-04
## PC7 -0.0007431548 -1.051640e-03 -4.346692e-04
## PC8 -0.0002118816 -5.243793e-04 1.006161e-04
## PC9 -0.0001761755 -4.985975e-04 1.462465e-04
## PC11 -0.0021135209 -2.464943e-03 -1.762099e-03
## PC12 -0.0017536810 -2.125771e-03 -1.381591e-03
## PC13 0.0011491789 7.712343e-04 1.527123e-03
## PC14 0.0009467031 5.559444e-04 1.337462e-03
## PC16 0.0013417027 9.419079e-04 1.741498e-03
## PC17 -0.0008029682 -1.227550e-03 -3.783867e-04
## PC18 -0.0014706461 -1.913809e-03 -1.027483e-03
## PC20 0.0017173999 1.229914e-03 2.204886e-03
## PC21 0.0002436889 -2.633654e-04 7.507433e-04
## PC22 0.0005313850 -2.621268e-04 1.324897e-03
## PC23 0.0012901432 3.129468e-04 2.267340e-03
## PC24 -0.0032796404 -4.428912e-03 -2.130369e-03
## PC25 0.0011063330 -1.757167e-04 2.388383e-03
## PC26 0.0014168399 9.744754e-05 2.736232e-03
## PC27 0.0015982836 2.710758e-04 2.925491e-03
## PC28 0.0006027089 -7.458642e-04 1.951282e-03
## PC29 0.0015286200 5.311022e-05 3.004130e-03
## PC31 -0.0009951147 -2.614946e-03 6.247170e-04
## PC32 -0.0027512834 -4.387171e-03 -1.115396e-03
## PC33 0.0012921149 -3.804795e-04 2.964709e-03
## PC34 0.0040388349 2.271057e-03 5.806613e-03
## PC37 -0.0013890918 -3.368627e-03 5.904436e-04
## PC38 0.0011074596 -9.527628e-04 3.167682e-03
## PC44 0.0017152667 -4.707702e-04 3.901304e-03
## PC45 -0.0013005600 -3.489601e-03 8.884812e-04
## PC47 -0.0015957827 -3.833214e-03 6.416481e-04
## PC48 0.0012556465 -1.026536e-03 3.537829e-03
## PC49 0.0011123770 -1.175229e-03 3.399983e-03
## PC57 -0.0016637368 -4.069017e-03 7.415431e-04
## PC59 0.0024513197 7.462271e-05 4.828017e-03
## PC60 -0.0013234917 -3.749661e-03 1.102678e-03
## PC63 -0.0021920542 -4.637903e-03 2.537943e-04
## PC64 -0.0019720970 -4.428624e-03 4.844301e-04
## PC65 -0.0011485676 -3.599165e-03 1.302029e-03
## PC66 -0.0023344523 -4.817857e-03 1.489525e-04
## PC68 0.0026013386 9.894665e-05 5.103731e-03
## PC69 0.0016019835 -9.139311e-04 4.117898e-03
## PC71 0.0028849599 3.688310e-04 5.401089e-03
## PC74 -0.0016045929 -4.171966e-03 9.627805e-04
## PC75 -0.0034056174 -5.987307e-03 -8.239278e-04
## PC77 0.0017444035 -8.409127e-04 4.329720e-03
## PC78 0.0014906992 -1.104279e-03 4.085678e-03
## PC79 0.0024646909 -1.554206e-04 5.084802e-03
## PC80 -0.0012272159 -3.891748e-03 1.437317e-03
## PC81 0.0038008121 1.145317e-03 6.456307e-03
## PC83 -0.0025461363 -5.197721e-03 1.054481e-04
## PC84 0.0034510898 7.845560e-04 6.117624e-03
## PC85 0.0046356082 1.929448e-03 7.341768e-03
## PC86 -0.0021140182 -4.813685e-03 5.856487e-04
## PC87 0.0079917487 5.259955e-03 1.072354e-02
## PC88 -0.0019045359 -4.675823e-03 8.667510e-04
## PC89 -0.0025765316 -5.301423e-03 1.483598e-04
## PC90 -0.0019874258 -4.724691e-03 7.498397e-04
## PC94 -0.0037782715 -6.542931e-03 -1.013612e-03
## PC96 -0.0038403925 -6.644133e-03 -1.036652e-03
## PC97 -0.0018094836 -4.596880e-03 9.779123e-04
## PC99 -0.0021723584 -4.974145e-03 6.294277e-04
## PC102 -0.0024153961 -5.255351e-03 4.245584e-04
## PC103 0.0028025654 -1.507000e-05 5.620201e-03
## PC104 -0.0037283368 -6.556930e-03 -8.997441e-04
## PC105 0.0030271855 1.888463e-04 5.865525e-03
## PC106 0.0036465850 8.213900e-04 6.471780e-03
## PC107 0.0012164069 -1.615229e-03 4.048043e-03
## PC109 0.0021445414 -7.014383e-04 4.990521e-03
## PC111 -0.0033480307 -6.212560e-03 -4.835014e-04
## PC113 0.0016276097 -1.241969e-03 4.497188e-03
## PC114 -0.0028422939 -5.706122e-03 2.153468e-05
## PC115 -0.0057720542 -8.656378e-03 -2.887730e-03
## PC118 0.0023483540 -5.493700e-04 5.246078e-03
## PC119 -0.0028879482 -5.781806e-03 5.910083e-06
## PC122 0.0025859779 -3.270246e-04 5.498980e-03
## PC123 -0.0024398312 -5.358963e-03 4.793004e-04
## PC124 0.0016884637 -1.237151e-03 4.614079e-03
## PC125 0.0020562283 -8.782947e-04 4.990751e-03
## PC127 0.0023169044 -5.861867e-04 5.219995e-03
## PC128 -0.0019080380 -4.835402e-03 1.019326e-03
## PC131 -0.0039830944 -6.925845e-03 -1.040343e-03
## PC133 -0.0014171974 -4.370144e-03 1.535750e-03
## PC134 0.0045785462 1.647384e-03 7.509709e-03
## PC135 0.0030155686 7.197429e-05 5.959163e-03
## PC138 0.0018387452 -1.142617e-03 4.820108e-03
## PC139 -0.0034859165 -6.452569e-03 -5.192640e-04
## PC143 0.0020890014 -9.103155e-04 5.088318e-03
## PC144 0.0025042869 -4.868277e-04 5.495401e-03
## PC145 0.0017490944 -1.253714e-03 4.751903e-03
## PC146 0.0046938976 1.679202e-03 7.708593e-03
## PC148 -0.0020388941 -5.021753e-03 9.439644e-04
## PC151 0.0030104170 -2.335209e-05 6.044186e-03
## PC153 0.0033871778 3.669846e-04 6.407371e-03
## PC154 -0.0036129566 -6.648374e-03 -5.775390e-04
## PC155 0.0032444401 2.058263e-04 6.283054e-03
## PC156 0.0033817945 3.344581e-04 6.429131e-03
## PC159 0.0057040318 2.664389e-03 8.743675e-03
## PC161 0.0015546860 -1.486372e-03 4.595744e-03
## PC162 -0.0051450187 -8.221766e-03 -2.068271e-03
## PC163 0.0025833525 -4.850980e-04 5.651803e-03Test
if (algo.stepwise.caret == TRUE){
test.model(model.stepwise, data.test
,method = 'leapSeq',subopt = NULL
,formula = formula, feature.names = feature.names, label.names = label.names
,id = id
,draw.limits = TRUE, transformation = t)
}## [1] "Summary of predicted values: "
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 4.639 4.961 5.012 5.001 5.049 5.143
## [1] "leapSeq Test MSE: 0.013858057909617"
## [1] "leapSeq Test RMSE: 0.11772025275889"
## [1] "leapSeq Test MSE (Org Scale): 82.2350242465771"
## [1] "leapSeq Test RMSE (Org Scale): 9.06835289601023"
LASSO with CV
Train
if (algo.LASSO.caret == TRUE){
set.seed(1)
tune.grid= expand.grid(alpha = 1,lambda = 10^seq(from=-4,to=-2,length=100))
returned = train.caret.glmselect(formula = formula
,data = data.train
,method = "glmnet"
,subopt = 'LASSO'
,tune.grid = tune.grid
,feature.names = feature.names)
model.LASSO.caret = returned$model
}## Aggregating results
## Selecting tuning parameters
## Fitting alpha = 1, lambda = 0.00102 on full training set
## glmnet
##
## 5584 samples
## 164 predictor
##
## No pre-processing
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 5026, 5026, 5026, 5025, 5025, 5026, ...
## Resampling results across tuning parameters:
##
## lambda RMSE Rsquared MAE
## 0.0001000000 0.1260825 0.2046718 0.09742207
## 0.0001047616 0.1260767 0.2047156 0.09741752
## 0.0001097499 0.1260708 0.2047609 0.09741279
## 0.0001149757 0.1260645 0.2048081 0.09740790
## 0.0001204504 0.1260582 0.2048560 0.09740292
## 0.0001261857 0.1260516 0.2049055 0.09739775
## 0.0001321941 0.1260448 0.2049569 0.09739235
## 0.0001384886 0.1260377 0.2050105 0.09738675
## 0.0001450829 0.1260303 0.2050659 0.09738098
## 0.0001519911 0.1260227 0.2051234 0.09737515
## 0.0001592283 0.1260148 0.2051830 0.09736920
## 0.0001668101 0.1260066 0.2052448 0.09736302
## 0.0001747528 0.1259980 0.2053104 0.09735658
## 0.0001830738 0.1259891 0.2053793 0.09734977
## 0.0001917910 0.1259797 0.2054517 0.09734272
## 0.0002009233 0.1259700 0.2055270 0.09733545
## 0.0002104904 0.1259600 0.2056047 0.09732812
## 0.0002205131 0.1259497 0.2056852 0.09732055
## 0.0002310130 0.1259390 0.2057689 0.09731291
## 0.0002420128 0.1259280 0.2058557 0.09730499
## 0.0002535364 0.1259168 0.2059431 0.09729703
## 0.0002656088 0.1259053 0.2060334 0.09728883
## 0.0002782559 0.1258934 0.2061281 0.09728025
## 0.0002915053 0.1258810 0.2062268 0.09727120
## 0.0003053856 0.1258682 0.2063303 0.09726176
## 0.0003199267 0.1258550 0.2064371 0.09725204
## 0.0003351603 0.1258415 0.2065464 0.09724210
## 0.0003511192 0.1258278 0.2066587 0.09723194
## 0.0003678380 0.1258139 0.2067727 0.09722197
## 0.0003853529 0.1257997 0.2068898 0.09721178
## 0.0004037017 0.1257851 0.2070103 0.09720176
## 0.0004229243 0.1257704 0.2071331 0.09719162
## 0.0004430621 0.1257553 0.2072603 0.09718129
## 0.0004641589 0.1257399 0.2073924 0.09717069
## 0.0004862602 0.1257243 0.2075271 0.09715995
## 0.0005094138 0.1257084 0.2076660 0.09714871
## 0.0005336699 0.1256923 0.2078087 0.09713750
## 0.0005590810 0.1256764 0.2079523 0.09712627
## 0.0005857021 0.1256604 0.2080982 0.09711571
## 0.0006135907 0.1256446 0.2082450 0.09710548
## 0.0006428073 0.1256296 0.2083851 0.09709652
## 0.0006734151 0.1256150 0.2085234 0.09708817
## 0.0007054802 0.1256009 0.2086592 0.09708034
## 0.0007390722 0.1255874 0.2087930 0.09707266
## 0.0007742637 0.1255748 0.2089201 0.09706635
## 0.0008111308 0.1255631 0.2090421 0.09706078
## 0.0008497534 0.1255529 0.2091508 0.09705710
## 0.0008902151 0.1255442 0.2092480 0.09705475
## 0.0009326033 0.1255385 0.2093165 0.09705483
## 0.0009770100 0.1255348 0.2093673 0.09705697
## 0.0010235310 0.1255337 0.2093957 0.09706146
## 0.0010722672 0.1255346 0.2094072 0.09706701
## 0.0011233240 0.1255399 0.2093726 0.09707475
## 0.0011768120 0.1255490 0.2093014 0.09708430
## 0.0012328467 0.1255613 0.2092006 0.09709614
## 0.0012915497 0.1255774 0.2090634 0.09711099
## 0.0013530478 0.1255955 0.2089150 0.09712797
## 0.0014174742 0.1256171 0.2087344 0.09714789
## 0.0014849683 0.1256417 0.2085341 0.09717050
## 0.0015556761 0.1256707 0.2082931 0.09719777
## 0.0016297508 0.1257016 0.2080455 0.09722851
## 0.0017073526 0.1257367 0.2077616 0.09726185
## 0.0017886495 0.1257707 0.2075144 0.09729153
## 0.0018738174 0.1258088 0.2072329 0.09732378
## 0.0019630407 0.1258486 0.2069499 0.09735462
## 0.0020565123 0.1258942 0.2066113 0.09738900
## 0.0021544347 0.1259445 0.2062318 0.09742628
## 0.0022570197 0.1260016 0.2057861 0.09746946
## 0.0023644894 0.1260615 0.2053221 0.09751627
## 0.0024770764 0.1261283 0.2047877 0.09756748
## 0.0025950242 0.1261999 0.2042033 0.09762418
## 0.0027185882 0.1262791 0.2035363 0.09768572
## 0.0028480359 0.1263649 0.2027990 0.09775115
## 0.0029836472 0.1264593 0.2019681 0.09782125
## 0.0031257158 0.1265548 0.2011568 0.09789386
## 0.0032745492 0.1266571 0.2002761 0.09797469
## 0.0034304693 0.1267602 0.1994136 0.09805780
## 0.0035938137 0.1268722 0.1984503 0.09814836
## 0.0037649358 0.1269875 0.1974720 0.09824250
## 0.0039442061 0.1271124 0.1963887 0.09834316
## 0.0041320124 0.1272433 0.1952556 0.09844567
## 0.0043287613 0.1273861 0.1939813 0.09855466
## 0.0045348785 0.1275330 0.1926951 0.09866591
## 0.0047508102 0.1276909 0.1912852 0.09878621
## 0.0049770236 0.1278541 0.1898300 0.09890973
## 0.0052140083 0.1280312 0.1881955 0.09904293
## 0.0054622772 0.1282237 0.1863484 0.09919031
## 0.0057223677 0.1284315 0.1842822 0.09935079
## 0.0059948425 0.1286470 0.1821334 0.09951832
## 0.0062802914 0.1288776 0.1797575 0.09969603
## 0.0065793322 0.1291204 0.1772135 0.09988561
## 0.0068926121 0.1293819 0.1743770 0.10008914
## 0.0072208090 0.1296552 0.1713683 0.10029652
## 0.0075646333 0.1299499 0.1679861 0.10051799
## 0.0079248290 0.1302446 0.1646172 0.10073492
## 0.0083021757 0.1305541 0.1609747 0.10096336
## 0.0086974900 0.1308615 0.1573733 0.10119179
## 0.0091116276 0.1311845 0.1534685 0.10143495
## 0.0095454846 0.1314959 0.1497763 0.10167206
## 0.0100000000 0.1318179 0.1458583 0.10191631
##
## Tuning parameter 'alpha' was held constant at a value of 1
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were alpha = 1 and lambda = 0.001023531.
## alpha lambda
## 51 1 0.001023531
## alpha lambda RMSE Rsquared MAE RMSESD RsquaredSD MAESD
## 1 1 0.0001000000 0.1260825 0.2046718 0.09742207 0.005468723 0.02236901 0.003236068
## 2 1 0.0001047616 0.1260767 0.2047156 0.09741752 0.005469059 0.02238403 0.003235452
## 3 1 0.0001097499 0.1260708 0.2047609 0.09741279 0.005469400 0.02239956 0.003234806
## 4 1 0.0001149757 0.1260645 0.2048081 0.09740790 0.005469750 0.02241571 0.003234135
## 5 1 0.0001204504 0.1260582 0.2048560 0.09740292 0.005470043 0.02243135 0.003233384
## 6 1 0.0001261857 0.1260516 0.2049055 0.09739775 0.005470325 0.02244778 0.003232585
## 7 1 0.0001321941 0.1260448 0.2049569 0.09739235 0.005470549 0.02246373 0.003231665
## 8 1 0.0001384886 0.1260377 0.2050105 0.09738675 0.005470760 0.02247970 0.003230658
## 9 1 0.0001450829 0.1260303 0.2050659 0.09738098 0.005470969 0.02249613 0.003229564
## 10 1 0.0001519911 0.1260227 0.2051234 0.09737515 0.005471189 0.02251318 0.003228480
## 11 1 0.0001592283 0.1260148 0.2051830 0.09736920 0.005471406 0.02253119 0.003227360
## 12 1 0.0001668101 0.1260066 0.2052448 0.09736302 0.005471630 0.02255043 0.003226204
## 13 1 0.0001747528 0.1259980 0.2053104 0.09735658 0.005471890 0.02257141 0.003225041
## 14 1 0.0001830738 0.1259891 0.2053793 0.09734977 0.005472167 0.02259350 0.003223823
## 15 1 0.0001917910 0.1259797 0.2054517 0.09734272 0.005472486 0.02261693 0.003222536
## 16 1 0.0002009233 0.1259700 0.2055270 0.09733545 0.005472835 0.02264126 0.003221237
## 17 1 0.0002104904 0.1259600 0.2056047 0.09732812 0.005473159 0.02266722 0.003220013
## 18 1 0.0002205131 0.1259497 0.2056852 0.09732055 0.005473483 0.02269446 0.003218792
## 19 1 0.0002310130 0.1259390 0.2057689 0.09731291 0.005473837 0.02272310 0.003217232
## 20 1 0.0002420128 0.1259280 0.2058557 0.09730499 0.005474230 0.02275304 0.003215534
## 21 1 0.0002535364 0.1259168 0.2059431 0.09729703 0.005474525 0.02278199 0.003213447
## 22 1 0.0002656088 0.1259053 0.2060334 0.09728883 0.005474803 0.02281248 0.003211119
## 23 1 0.0002782559 0.1258934 0.2061281 0.09728025 0.005474981 0.02284316 0.003208638
## 24 1 0.0002915053 0.1258810 0.2062268 0.09727120 0.005475135 0.02287516 0.003206036
## 25 1 0.0003053856 0.1258682 0.2063303 0.09726176 0.005475155 0.02290682 0.003203253
## 26 1 0.0003199267 0.1258550 0.2064371 0.09725204 0.005475209 0.02293929 0.003200312
## 27 1 0.0003351603 0.1258415 0.2065464 0.09724210 0.005475598 0.02297395 0.003197246
## 28 1 0.0003511192 0.1258278 0.2066587 0.09723194 0.005476096 0.02300981 0.003194303
## 29 1 0.0003678380 0.1258139 0.2067727 0.09722197 0.005476928 0.02304752 0.003191193
## 30 1 0.0003853529 0.1257997 0.2068898 0.09721178 0.005477806 0.02308594 0.003187963
## 31 1 0.0004037017 0.1257851 0.2070103 0.09720176 0.005478945 0.02312617 0.003184618
## 32 1 0.0004229243 0.1257704 0.2071331 0.09719162 0.005480205 0.02316812 0.003181095
## 33 1 0.0004430621 0.1257553 0.2072603 0.09718129 0.005481915 0.02321066 0.003177424
## 34 1 0.0004641589 0.1257399 0.2073924 0.09717069 0.005483676 0.02325166 0.003173594
## 35 1 0.0004862602 0.1257243 0.2075271 0.09715995 0.005485119 0.02328592 0.003169007
## 36 1 0.0005094138 0.1257084 0.2076660 0.09714871 0.005486564 0.02331956 0.003164249
## 37 1 0.0005336699 0.1256923 0.2078087 0.09713750 0.005487599 0.02335295 0.003159006
## 38 1 0.0005590810 0.1256764 0.2079523 0.09712627 0.005488686 0.02339021 0.003153440
## 39 1 0.0005857021 0.1256604 0.2080982 0.09711571 0.005489928 0.02343134 0.003146378
## 40 1 0.0006135907 0.1256446 0.2082450 0.09710548 0.005491300 0.02347601 0.003139060
## 41 1 0.0006428073 0.1256296 0.2083851 0.09709652 0.005493340 0.02352508 0.003131897
## 42 1 0.0006734151 0.1256150 0.2085234 0.09708817 0.005495410 0.02357576 0.003123739
## 43 1 0.0007054802 0.1256009 0.2086592 0.09708034 0.005496740 0.02361655 0.003114351
## 44 1 0.0007390722 0.1255874 0.2087930 0.09707266 0.005498020 0.02365332 0.003104944
## 45 1 0.0007742637 0.1255748 0.2089201 0.09706635 0.005500343 0.02369586 0.003096681
## 46 1 0.0008111308 0.1255631 0.2090421 0.09706078 0.005502852 0.02373917 0.003088597
## 47 1 0.0008497534 0.1255529 0.2091508 0.09705710 0.005505630 0.02378900 0.003081498
## 48 1 0.0008902151 0.1255442 0.2092480 0.09705475 0.005508493 0.02384071 0.003073773
## 49 1 0.0009326033 0.1255385 0.2093165 0.09705483 0.005511910 0.02388925 0.003066434
## 50 1 0.0009770100 0.1255348 0.2093673 0.09705697 0.005515382 0.02394078 0.003060203
## 51 1 0.0010235310 0.1255337 0.2093957 0.09706146 0.005518812 0.02399187 0.003053976
## 52 1 0.0010722672 0.1255346 0.2094072 0.09706701 0.005522158 0.02404079 0.003047697
## 53 1 0.0011233240 0.1255399 0.2093726 0.09707475 0.005525456 0.02407587 0.003041392
## 54 1 0.0011768120 0.1255490 0.2093014 0.09708430 0.005529051 0.02411405 0.003035638
## 55 1 0.0012328467 0.1255613 0.2092006 0.09709614 0.005534578 0.02417738 0.003033481
## 56 1 0.0012915497 0.1255774 0.2090634 0.09711099 0.005540552 0.02424070 0.003031494
## 57 1 0.0013530478 0.1255955 0.2089150 0.09712797 0.005546234 0.02430813 0.003029750
## 58 1 0.0014174742 0.1256171 0.2087344 0.09714789 0.005551959 0.02437253 0.003029249
## 59 1 0.0014849683 0.1256417 0.2085341 0.09717050 0.005560154 0.02443063 0.003031508
## 60 1 0.0015556761 0.1256707 0.2082931 0.09719777 0.005569661 0.02448043 0.003033078
## 61 1 0.0016297508 0.1257016 0.2080455 0.09722851 0.005580272 0.02452286 0.003032948
## 62 1 0.0017073526 0.1257367 0.2077616 0.09726185 0.005591886 0.02456525 0.003033655
## 63 1 0.0017886495 0.1257707 0.2075144 0.09729153 0.005603542 0.02466919 0.003034926
## 64 1 0.0018738174 0.1258088 0.2072329 0.09732378 0.005615403 0.02477067 0.003036598
## 65 1 0.0019630407 0.1258486 0.2069499 0.09735462 0.005626519 0.02490640 0.003038752
## 66 1 0.0020565123 0.1258942 0.2066113 0.09738900 0.005637251 0.02502849 0.003039624
## 67 1 0.0021544347 0.1259445 0.2062318 0.09742628 0.005648284 0.02512498 0.003040915
## 68 1 0.0022570197 0.1260016 0.2057861 0.09746946 0.005660299 0.02521097 0.003041832
## 69 1 0.0023644894 0.1260615 0.2053221 0.09751627 0.005669783 0.02524201 0.003043284
## 70 1 0.0024770764 0.1261283 0.2047877 0.09756748 0.005678586 0.02523420 0.003044600
## 71 1 0.0025950242 0.1261999 0.2042033 0.09762418 0.005682640 0.02512431 0.003044469
## 72 1 0.0027185882 0.1262791 0.2035363 0.09768572 0.005686554 0.02498208 0.003046624
## 73 1 0.0028480359 0.1263649 0.2027990 0.09775115 0.005691829 0.02481281 0.003051511
## 74 1 0.0029836472 0.1264593 0.2019681 0.09782125 0.005697492 0.02462696 0.003054682
## 75 1 0.0031257158 0.1265548 0.2011568 0.09789386 0.005703922 0.02454317 0.003059049
## 76 1 0.0032745492 0.1266571 0.2002761 0.09797469 0.005709961 0.02444007 0.003060940
## 77 1 0.0034304693 0.1267602 0.1994136 0.09805780 0.005714504 0.02440549 0.003065936
## 78 1 0.0035938137 0.1268722 0.1984503 0.09814836 0.005718712 0.02436154 0.003069996
## 79 1 0.0037649358 0.1269875 0.1974720 0.09824250 0.005716502 0.02430181 0.003067797
## 80 1 0.0039442061 0.1271124 0.1963887 0.09834316 0.005712351 0.02419828 0.003061138
## 81 1 0.0041320124 0.1272433 0.1952556 0.09844567 0.005705121 0.02405859 0.003051228
## 82 1 0.0043287613 0.1273861 0.1939813 0.09855466 0.005698734 0.02387929 0.003043569
## 83 1 0.0045348785 0.1275330 0.1926951 0.09866591 0.005692840 0.02375917 0.003038266
## 84 1 0.0047508102 0.1276909 0.1912852 0.09878621 0.005687934 0.02362865 0.003034210
## 85 1 0.0049770236 0.1278541 0.1898300 0.09890973 0.005679072 0.02348158 0.003028450
## 86 1 0.0052140083 0.1280312 0.1881955 0.09904293 0.005669511 0.02329129 0.003022277
## 87 1 0.0054622772 0.1282237 0.1863484 0.09919031 0.005655903 0.02298977 0.003013228
## 88 1 0.0057223677 0.1284315 0.1842822 0.09935079 0.005640721 0.02262829 0.003003959
## 89 1 0.0059948425 0.1286470 0.1821334 0.09951832 0.005625468 0.02233746 0.002997386
## 90 1 0.0062802914 0.1288776 0.1797575 0.09969603 0.005610533 0.02196863 0.002992295
## 91 1 0.0065793322 0.1291204 0.1772135 0.09988561 0.005599032 0.02165368 0.002992005
## 92 1 0.0068926121 0.1293819 0.1743770 0.10008914 0.005588324 0.02132520 0.002990617
## 93 1 0.0072208090 0.1296552 0.1713683 0.10029652 0.005573148 0.02105525 0.002986774
## 94 1 0.0075646333 0.1299499 0.1679861 0.10051799 0.005556051 0.02075031 0.002980449
## 95 1 0.0079248290 0.1302446 0.1646172 0.10073492 0.005537806 0.02051751 0.002976055
## 96 1 0.0083021757 0.1305541 0.1609747 0.10096336 0.005521288 0.02023450 0.002974015
## 97 1 0.0086974900 0.1308615 0.1573733 0.10119179 0.005500597 0.01994873 0.002967727
## 98 1 0.0091116276 0.1311845 0.1534685 0.10143495 0.005479771 0.01954826 0.002952125
## 99 1 0.0095454846 0.1314959 0.1497763 0.10167206 0.005456415 0.01915786 0.002930001
## 100 1 0.0100000000 0.1318179 0.1458583 0.10191631 0.005433767 0.01862530 0.002906214
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## [1] "Coefficients"
## model.coef
## (Intercept) 5.001487e+00
## PC1 -1.567812e-03
## PC2 -3.493388e-03
## PC3 -1.446555e-03
## PC4 -1.129211e-03
## PC5 6.832443e-04
## PC6 -3.535998e-04
## PC7 -6.479233e-04
## PC8 -9.431297e-05
## PC9 -7.560733e-05
## PC11 -1.986916e-03
## PC12 -1.646537e-03
## PC13 1.031739e-03
## PC14 8.286380e-04
## PC16 1.218077e-03
## PC17 -6.625690e-04
## PC18 -1.331233e-03
## PC20 1.562215e-03
## PC21 9.138747e-05
## PC22 2.633970e-04
## PC23 9.951633e-04
## PC24 -2.923723e-03
## PC25 6.556743e-04
## PC26 1.043674e-03
## PC27 1.190914e-03
## PC28 1.988490e-04
## PC29 1.081735e-03
## PC31 -4.993303e-04
## PC32 -2.243598e-03
## PC33 7.243084e-04
## PC34 3.488786e-03
## PC37 -7.877621e-04
## PC38 5.062938e-04
## PC44 9.732651e-04
## PC45 -5.988759e-04
## PC47 -8.665171e-04
## PC48 5.176597e-04
## PC49 3.980649e-04
## PC51 5.233114e-05
## PC57 -9.055802e-04
## PC58 1.027779e-04
## PC59 1.674679e-03
## PC60 -4.742266e-04
## PC63 -1.446109e-03
## PC64 -1.152212e-03
## PC65 -3.452139e-04
## PC66 -1.486194e-03
## PC68 1.875676e-03
## PC69 6.968924e-04
## PC71 2.099835e-03
## PC73 9.164869e-05
## PC74 -8.155097e-04
## PC75 -2.531314e-03
## PC77 9.025942e-04
## PC78 6.248711e-04
## PC79 1.606224e-03
## PC80 -3.147085e-04
## PC81 2.972511e-03
## PC83 -1.781444e-03
## PC84 2.622673e-03
## PC85 3.721049e-03
## PC86 -1.259845e-03
## PC87 7.057308e-03
## PC88 -9.870596e-04
## PC89 -1.646929e-03
## PC90 -1.071178e-03
## PC94 -2.892807e-03
## PC96 -2.865481e-03
## PC97 -8.956921e-04
## PC98 -1.460496e-04
## PC99 -1.300748e-03
## PC102 -1.445495e-03
## PC103 1.866757e-03
## PC104 -2.802670e-03
## PC105 2.141194e-03
## PC106 2.722359e-03
## PC107 3.387021e-04
## PC109 1.185912e-03
## PC111 -2.291964e-03
## PC113 6.320066e-04
## PC114 -1.879096e-03
## PC115 -4.902552e-03
## PC118 1.455565e-03
## PC119 -1.946489e-03
## PC120 1.913643e-04
## PC122 1.619960e-03
## PC123 -1.432900e-03
## PC124 7.632978e-04
## PC125 1.113433e-03
## PC127 1.413671e-03
## PC128 -1.053886e-03
## PC131 -3.044589e-03
## PC132 1.754724e-04
## PC133 -5.653046e-04
## PC134 3.634871e-03
## PC135 2.042061e-03
## PC136 3.101532e-04
## PC137 -3.647538e-06
## PC138 9.023092e-04
## PC139 -2.505786e-03
## PC140 -3.107734e-04
## PC143 9.772412e-04
## PC144 1.547501e-03
## PC145 9.053174e-04
## PC146 3.694168e-03
## PC147 -5.613169e-05
## PC148 -1.095390e-03
## PC151 2.012338e-03
## PC153 2.277421e-03
## PC154 -2.595253e-03
## PC155 2.353435e-03
## PC156 2.482936e-03
## PC159 4.829031e-03
## PC161 5.273463e-04
## PC162 -4.226100e-03
## PC163 1.597400e-03Test
if (algo.LASSO.caret == TRUE){
test.model(model.LASSO.caret, data.test
,method = 'glmnet',subopt = "LASSO"
,formula = formula, feature.names = feature.names, label.names = label.names
,draw.limits = TRUE, transformation = t)
}## [1] "Summary of predicted values: "
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 4.698 4.966 5.012 5.001 5.046 5.125
## [1] "glmnet LASSO Test MSE: 0.0137364202892418"
## [1] "glmnet LASSO Test RMSE: 0.117202475610551"
## [1] "glmnet LASSO Test MSE (Org Scale): 81.5488598346235"
## [1] "glmnet LASSO Test RMSE (Org Scale): 9.03044073313277"
LARS with CV
Train
if (algo.LARS.caret == TRUE){
set.seed(1)
returned = train.caret.glmselect(formula = formula
,data = data.train
,method = "lars"
,subopt = 'NULL'
,feature.names = feature.names)
model.LARS.caret = returned$model
}## Warning in nominalTrainWorkflow(x = x, y = y, wts = weights, info = trainInfo, : There were missing values in resampled
## performance measures.## Aggregating results
## Selecting tuning parameters
## Fitting fraction = 0.727 on full training set
## Least Angle Regression
##
## 5584 samples
## 164 predictor
##
## Pre-processing: centered (164), scaled (164)
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 5026, 5026, 5026, 5025, 5025, 5026, ...
## Resampling results across tuning parameters:
##
## fraction RMSE Rsquared MAE
## 0.00000000 0.1410824 NaN 0.10856265
## 0.01010101 0.1396190 0.08479660 0.10753014
## 0.02020202 0.1383496 0.08479660 0.10662638
## 0.03030303 0.1372793 0.08479660 0.10586782
## 0.04040404 0.1364220 0.08507658 0.10525349
## 0.05050505 0.1357349 0.09462889 0.10476920
## 0.06060606 0.1351147 0.10371154 0.10433708
## 0.07070707 0.1345335 0.11191090 0.10392114
## 0.08080808 0.1339773 0.11952394 0.10351470
## 0.09090909 0.1334533 0.12640891 0.10312749
## 0.10101010 0.1329667 0.13235060 0.10276612
## 0.11111111 0.1325370 0.13736321 0.10244916
## 0.12121212 0.1321326 0.14211319 0.10214952
## 0.13131313 0.1317426 0.14684531 0.10185521
## 0.14141414 0.1313730 0.15130900 0.10157582
## 0.15151515 0.1310213 0.15546194 0.10130976
## 0.16161616 0.1306822 0.15951206 0.10105631
## 0.17171717 0.1303581 0.16330128 0.10081820
## 0.18181818 0.1300486 0.16687014 0.10058924
## 0.19191919 0.1297470 0.17031546 0.10036436
## 0.20202020 0.1294549 0.17359608 0.10014450
## 0.21212121 0.1291762 0.17664077 0.09992976
## 0.22222222 0.1289202 0.17933752 0.09972863
## 0.23232323 0.1286815 0.18178665 0.09954440
## 0.24242424 0.1284530 0.18409640 0.09936805
## 0.25252525 0.1282385 0.18622319 0.09920272
## 0.26262626 0.1280456 0.18808192 0.09905471
## 0.27272727 0.1278731 0.18966457 0.09892508
## 0.28282828 0.1277165 0.19104937 0.09880806
## 0.29292929 0.1275687 0.19236514 0.09869474
## 0.30303030 0.1274335 0.19355952 0.09859085
## 0.31313131 0.1273096 0.19464270 0.09849490
## 0.32323232 0.1271940 0.19564758 0.09840508
## 0.33333333 0.1270858 0.19660302 0.09831958
## 0.34343434 0.1269869 0.19745068 0.09823938
## 0.35353535 0.1268943 0.19823921 0.09816448
## 0.36363636 0.1268057 0.19900288 0.09809086
## 0.37373737 0.1267219 0.19972742 0.09802236
## 0.38383838 0.1266426 0.20040861 0.09795984
## 0.39393939 0.1265682 0.20103959 0.09790044
## 0.40404040 0.1264955 0.20167453 0.09784403
## 0.41414141 0.1264258 0.20229332 0.09779194
## 0.42424242 0.1263631 0.20283250 0.09774520
## 0.43434343 0.1263038 0.20333804 0.09770114
## 0.44444444 0.1262482 0.20380446 0.09765806
## 0.45454545 0.1261959 0.20424267 0.09761648
## 0.46464646 0.1261474 0.20463777 0.09757743
## 0.47474747 0.1261016 0.20500433 0.09754201
## 0.48484848 0.1260573 0.20536102 0.09750848
## 0.49494949 0.1260167 0.20567547 0.09747754
## 0.50505051 0.1259778 0.20597735 0.09744764
## 0.51515152 0.1259409 0.20626145 0.09742004
## 0.52525253 0.1259067 0.20651668 0.09739453
## 0.53535354 0.1258739 0.20676453 0.09736963
## 0.54545455 0.1258437 0.20698811 0.09734732
## 0.55555556 0.1258159 0.20718672 0.09732584
## 0.56565657 0.1257890 0.20738323 0.09730370
## 0.57575758 0.1257630 0.20757568 0.09728164
## 0.58585859 0.1257376 0.20776859 0.09725977
## 0.59595960 0.1257128 0.20796257 0.09723711
## 0.60606061 0.1256890 0.20815266 0.09721335
## 0.61616162 0.1256663 0.20833647 0.09719058
## 0.62626263 0.1256464 0.20849136 0.09717154
## 0.63636364 0.1256280 0.20863479 0.09715516
## 0.64646465 0.1256101 0.20878348 0.09713951
## 0.65656566 0.1255937 0.20891792 0.09712466
## 0.66666667 0.1255792 0.20903685 0.09711118
## 0.67676768 0.1255655 0.20915252 0.09709860
## 0.68686869 0.1255535 0.20925350 0.09708776
## 0.69696970 0.1255440 0.20933102 0.09707866
## 0.70707071 0.1255367 0.20938725 0.09707057
## 0.71717172 0.1255322 0.20941496 0.09706376
## 0.72727273 0.1255315 0.20940298 0.09705871
## 0.73737374 0.1255332 0.20937069 0.09705461
## 0.74747475 0.1255364 0.20932651 0.09705262
## 0.75757576 0.1255426 0.20925415 0.09705270
## 0.76767677 0.1255520 0.20914958 0.09705575
## 0.77777778 0.1255636 0.20902710 0.09706000
## 0.78787879 0.1255774 0.20888612 0.09706624
## 0.79797980 0.1255932 0.20872953 0.09707492
## 0.80808081 0.1256106 0.20856140 0.09708471
## 0.81818182 0.1256296 0.20838106 0.09709555
## 0.82828283 0.1256505 0.20818702 0.09710848
## 0.83838384 0.1256740 0.20797185 0.09712385
## 0.84848485 0.1256984 0.20775283 0.09714107
## 0.85858586 0.1257239 0.20752938 0.09715873
## 0.86868687 0.1257506 0.20730056 0.09717707
## 0.87878788 0.1257787 0.20706336 0.09719647
## 0.88888889 0.1258077 0.20682243 0.09721685
## 0.89898990 0.1258381 0.20657332 0.09723906
## 0.90909091 0.1258704 0.20631055 0.09726306
## 0.91919192 0.1259032 0.20604827 0.09728710
## 0.92929293 0.1259371 0.20578231 0.09731117
## 0.93939394 0.1259726 0.20550522 0.09733714
## 0.94949495 0.1260093 0.20522318 0.09736487
## 0.95959596 0.1260464 0.20494349 0.09739350
## 0.96969697 0.1260854 0.20464862 0.09742430
## 0.97979798 0.1261263 0.20434020 0.09745741
## 0.98989899 0.1261680 0.20403005 0.09749160
## 1.00000000 0.1262107 0.20371699 0.09752633
##
## RMSE was used to select the optimal model using the smallest value.
## The final value used for the model was fraction = 0.7272727.
## fraction
## 73 0.7272727## Warning: Removed 1 rows containing missing values (geom_point).
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## [1] "Coefficients"
## PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8
## -1.807777e-02 -3.974089e-02 -1.641502e-02 -1.259014e-02 7.354240e-03 -3.806200e-03 -6.818266e-03 -9.759112e-04
## PC9 PC11 PC12 PC13 PC14 PC16 PC17 PC18
## -7.576262e-04 -1.836135e-02 -1.436554e-02 8.861464e-03 6.884288e-03 9.887667e-03 -5.061638e-03 -9.755651e-03
## PC20 PC21 PC22 PC23 PC24 PC25 PC26 PC27
## 1.040368e-02 5.814544e-04 1.073440e-03 3.303890e-03 -8.262577e-03 1.657465e-03 2.566088e-03 2.910117e-03
## PC28 PC29 PC31 PC32 PC33 PC34 PC37 PC38
## 4.753624e-04 2.377255e-03 -9.977010e-04 -4.454384e-03 1.402403e-03 6.408199e-03 -1.288745e-03 7.947756e-04
## PC44 PC45 PC47 PC48 PC49 PC51 PC57 PC58
## 1.442167e-03 -8.847126e-04 -1.254266e-03 7.330733e-04 5.615982e-04 6.949503e-05 -1.219430e-03 1.360983e-04
## PC59 PC60 PC63 PC64 PC65 PC66 PC68 PC69
## 2.285265e-03 -6.316474e-04 -1.915560e-03 -1.520356e-03 -4.537592e-04 -1.939916e-03 2.430650e-03 8.953422e-04
## PC71 PC73 PC74 PC75 PC77 PC78 PC79 PC80
## 2.707261e-03 1.130220e-04 -1.028108e-03 -3.182552e-03 1.130317e-03 7.781756e-04 1.987858e-03 -3.790135e-04
## PC81 PC83 PC84 PC85 PC86 PC87 PC88 PC89
## 3.634402e-03 -2.179009e-03 3.190434e-03 4.465104e-03 -1.511251e-03 8.388655e-03 -1.153598e-03 -1.959136e-03
## PC90 PC94 PC96 PC97 PC98 PC99 PC102 PC103
## -1.266890e-03 -3.393798e-03 -3.316230e-03 -1.039651e-03 -1.656034e-04 -1.504194e-03 -1.649463e-03 2.148357e-03
## PC104 PC105 PC106 PC107 PC109 PC111 PC113 PC114
## -3.214853e-03 2.446588e-03 3.126311e-03 3.846943e-04 1.349347e-03 -2.594311e-03 7.110745e-04 -2.126160e-03
## PC115 PC118 PC119 PC120 PC122 PC123 PC124 PC125
## -5.522405e-03 1.627782e-03 -2.180681e-03 2.113176e-04 1.802282e-03 -1.590026e-03 8.440231e-04 1.228383e-03
## PC127 PC128 PC131 PC132 PC133 PC134 PC135 PC136
## 1.578087e-03 -1.165117e-03 -3.356972e-03 1.895286e-04 -6.182413e-04 4.022129e-03 2.248923e-03 3.351567e-04
## PC138 PC139 PC140 PC143 PC144 PC145 PC146 PC147
## 9.799095e-04 -2.740022e-03 -3.325096e-04 1.053795e-03 1.676228e-03 9.755513e-04 3.976309e-03 -5.701974e-05
## PC148 PC151 PC153 PC154 PC155 PC156 PC159 PC161
## -1.188738e-03 2.150972e-03 2.444114e-03 -2.772852e-03 2.512345e-03 2.643782e-03 5.154754e-03 5.587627e-04
## PC162 PC163
## -4.459427e-03 1.686526e-03Test
if (algo.LARS.caret == TRUE){
test.model(model.LARS.caret, data.test
,method = 'lars',subopt = NULL
,formula = formula, feature.names = feature.names, label.names = label.names
,draw.limits = TRUE, transformation = t)
}## [1] "Summary of predicted values: "
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 4.699 4.966 5.012 5.001 5.046 5.125
## [1] "lars Test MSE: 0.0137364263489851"
## [1] "lars Test RMSE: 0.117202501462149"
## [1] "lars Test MSE (Org Scale): 81.5488137763212"
## [1] "lars Test RMSE (Org Scale): 9.03043818296328"
Session Info
sessionInfo()## R version 3.5.1 (2018-07-02)
## Platform: x86_64-w64-mingw32/x64 (64-bit)
## Running under: Windows 10 x64 (build 17134)
##
## Matrix products: default
##
## locale:
## [1] LC_COLLATE=English_United States.1252 LC_CTYPE=English_United States.1252 LC_MONETARY=English_United States.1252
## [4] LC_NUMERIC=C LC_TIME=English_United States.1252
##
## attached base packages:
## [1] parallel stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] bindrcpp_0.2.2 knitr_1.20 htmltools_0.3.6 reshape2_1.4.3
## [5] lars_1.2 doParallel_1.0.14 iterators_1.0.10 caret_6.0-81
## [9] leaps_3.0 ggforce_0.1.3 rlist_0.4.6.1 car_3.0-2
## [13] carData_3.0-2 bestNormalize_1.3.0 scales_1.0.0 onewaytests_2.0
## [17] caTools_1.17.1.1 mosaic_1.5.0 mosaicData_0.17.0 ggformula_0.9.1
## [21] ggstance_0.3.1 lattice_0.20-35 DT_0.5 ggiraph_0.6.0
## [25] investr_1.4.0 glmnet_2.0-16 foreach_1.4.4 Matrix_1.2-14
## [29] MASS_7.3-50 PerformanceAnalytics_1.5.2 xts_0.11-2 zoo_1.8-4
## [33] forcats_0.3.0 stringr_1.3.1 dplyr_0.7.8 purrr_0.2.5
## [37] readr_1.3.1 tidyr_0.8.2 tibble_1.4.2 ggplot2_3.1.0
## [41] tidyverse_1.2.1 usdm_1.1-18 raster_2.8-4 sp_1.3-1
## [45] pacman_0.5.0
##
## loaded via a namespace (and not attached):
## [1] readxl_1.2.0 backports_1.1.3 plyr_1.8.4 lazyeval_0.2.1 splines_3.5.1 mycor_0.1.1
## [7] crosstalk_1.0.0 leaflet_2.0.2 digest_0.6.18 magrittr_1.5 mosaicCore_0.6.0 openxlsx_4.1.0
## [13] recipes_0.1.4 modelr_0.1.2 gower_0.1.2 colorspace_1.3-2 rvest_0.3.2 ggrepel_0.8.0
## [19] haven_2.0.0 crayon_1.3.4 jsonlite_1.5 bindr_0.1.1 survival_2.42-3 glue_1.3.0
## [25] registry_0.5 gtable_0.2.0 ppcor_1.1 ipred_0.9-8 abind_1.4-5 rngtools_1.3.1
## [31] bibtex_0.4.2 Rcpp_1.0.0 xtable_1.8-3 units_0.6-2 foreign_0.8-70 stats4_3.5.1
## [37] lava_1.6.4 prodlim_2018.04.18 htmlwidgets_1.3 httr_1.4.0 RColorBrewer_1.1-2 pkgconfig_2.0.2
## [43] farver_1.1.0 nnet_7.3-12 labeling_0.3 tidyselect_0.2.5 rlang_0.3.1 later_0.7.5
## [49] munsell_0.5.0 cellranger_1.1.0 tools_3.5.1 cli_1.0.1 generics_0.0.2 moments_0.14
## [55] sjlabelled_1.0.17 broom_0.5.1 evaluate_0.12 ggdendro_0.1-20 yaml_2.2.0 ModelMetrics_1.2.2
## [61] zip_2.0.1 nlme_3.1-137 doRNG_1.7.1 mime_0.6 xml2_1.2.0 compiler_3.5.1
## [67] rstudioapi_0.8 curl_3.2 tweenr_1.0.1 stringi_1.2.4 gdtools_0.1.7 pillar_1.3.1
## [73] data.table_1.11.8 bitops_1.0-6 insight_0.1.2 httpuv_1.4.5 R6_2.3.0 promises_1.0.1
## [79] gridExtra_2.3 rio_0.5.16 codetools_0.2-15 assertthat_0.2.0 pkgmaker_0.27 withr_2.1.2
## [85] nortest_1.0-4 mgcv_1.8-24 hms_0.4.2 quadprog_1.5-5 grid_3.5.1 rpart_4.1-13
## [91] timeDate_3043.102 class_7.3-14 rmarkdown_1.11 shiny_1.2.0 lubridate_1.7.4